Introduction to r for quantitative finance pdf download

So the right to enter at zero cost into a forward contract with delivery price K equals the right to buy a stock for K. Whilst European options on forwards are equal in value to European options on the underlying asset, American options on the forward contract can have different character- istics to American options on the asset.

American options on forward contracts are equal in value to European options on for- ward contracts, which are equal in value to European options on the underlying asset.

American puts on the underlying asset will, however, typically have greater value. Proof We will prove the result for puts. If the American put is exercised early, then the portfolio now consists of long one forward contract with delivery price K and maturity T , long one European put on the forward contract and some cash.

We can exercise the European put at T to go short an identical contract. Therefore, we have an arbitrage portfolio. This argument is similar to the reasoning why an American call on a stock paying no dividends has price equal to that of the European.

However, the American put on a stock has price greater than or equal to the European put. The implicit strike on our option-on-the-forward is zero. The option is to enter the for- ward contract with delivery price K at zero cost.

The exercises provide further examples. Example Options on FRAs—called caplets and floorlets, which we encounter further in Chapter 12—are usually all specified as European style. Options on futures are more complex because of the variation margin of the contract, and thus are not strictly an option on a forward rate. American options on futures typically have slightly higher value than European options on futures.

Table 7. Using put-call parity or otherwise, restate the call butterfly as a portfolio consisting solely of puts. Draw the payout of the condor, and express the condor as a portfolio consisting solely of call butterflies. Call spreads and digital options a Draw the payout profile for the following two call spread portfolios. Hint Exercising early means the strike price K will be received early. Consider under which environments this will be preferable. Prove, or find a counter example to, each.

A simple model, the one-step binomial tree, is rich enough to introduce and explore these key ideas. Consider a portfolio consisting of short one strike call and long units of stock. This reasoning is sometimes called a hedging argument, since we have con- structed a portfolio of the call option and stock that has no risk—is hedged—to movements in the stock price. A complementary approach is to consider a replication argument. There is a unique line connecting these points.

The hedging argument constructs a portfolio of stock and option that is hedged to any movement in the stock price, that is, it uses the option and stock to replicate the bond. The replication argument constructs a portfolio of stock and bond to replicate the option. We could equally use a portfolio of option and bond to replicate the stock. If the option price is different to the price given by the replication argument, then we can construct an arbitrage portfolio.

So the replication argument determines the only possible arbitrage-free price, though we have not yet shown that this price is in fact arbitrage-free. We explore this general case in the exercises.

You may want to write down the relevant arbitrage portfolios in these cases. Thus we have a remarkable result. We have shown that in this particular one-step two-state tree, the only possible arbitrage- free option price is the price given by risk-neutral pricing, that is, where prices are discounted expectations of payouts using the risk-neutral probability.

There is nothing special about the numbers we used in this example. We prove the general case in Question 3. In other words, risk-neutral pricing holds for all the assets. By linearity of expectation, this must also be true for any linear combination of assets. So, either the portfolio is identically zero at maturity or, if it has positive value at maturity with positive probability, then it must also have negative value at maturity with positive probability.

Therefore, it cannot be an arbitrage portfolio. Thus for the one-step binomial tree, if prices of contracts are discounted risk-neutral expected values, there can be no arbitrage. This argument holds regardless of the actual probability of an up move on the tree, since arbitrage is only defined using zero or non-zero probabilities.

So for the one-step binomial model, we have shown that the risk-neutral price is arbitrage-free. Summary The replication and risk-neutral pricing arguments we have explored in these two sections provide a powerful result. The replication argument determines that only one price can be free of arbitrage and that any other price is arbitrageable.

Risk-neutral pricing demonstrates that this replication price is indeed arbitrage-free. Therefore, we have obtained a unique arbitrage-free price. We extend these key arguments underlying quantitative finance to multiple time steps in the next section.

The arguments can also be extended to continuous-time models, although this theory is largely beyond our scope. However, in Chapter 10 we take the limit of the binomial tree and assume the arguments we developed in discrete time transfer to the continuous case.

We do not discuss the mathematical conditions required. We could vary these assumptions at each step without altering our conclusions. However, the arithmetic would become messier without increasing insight. We will apply similar replication arguments as before at states A and B. The option value at state B is trivially zero. At each node of the tree the stock could only move to two possible values, hence exact replication is possible.

Replication and risk-neutral pricing immediately extend to multiple binomial steps. We assume the probability of an up move and a down move are both non-zero. In Chapter 10 we will let T become small. We construct an arbitrage portfolio by borrow- ing S0 and buying one stock. We need to show that all such portfolios are arbitrage-free. Note that it is important for this argument that both states have non-zero probabilities.

Thus we have shown the equivalence of the replication and risk-neutral price in the general case. However, it is generally easier to take limits and work with continuous distributions. We do this in Chapter What is different to b? Arbitrage on the tree A stock that pays no dividends has price today of General two-state world A non-dividend paying stock has current price S0.

The annually compounded interest rate is a constant r. Hence calculate the discounted expected payout of the derivative under risk-neutral probabilities, and verify that your answer equals the replication price in b. What have we assumed about the actual probabilities of state A and state B?

Verify the price b makes sense. Again, verify the price b makes sense. The fundamental theorem precisely establishes the link between expected values and arbitrage-free prices.

If X0 ,. All processes we consider in this book are assumed to be Markov. The process Y0 ,. One can think of this as the price information known at time n. Martingales play an important role in probability theory and finance see the excellent Williams for a more detailed exposition.

We assume it holds for n — 1 and prove by induction. We have proof by induction. Recall that in Chapter 1 we defined Mn to be the value of the money market account. Mn Mm Therefore, we immediately have the following.

We see that risk-neutral pricing is equivalent to the statement that ratios of prices to the money market account are martingales under the risk-neutral probability. Fundamental theorem of asset pricing.

There are two important extensions to the fundamental theorem. First, under suitable conditions, the result holds for continuous-time models. We will not attempt to prove this extension, although we will take the limit of the binomial tree as the number of time steps tends to infinity and assume results carry over to this limit. The general theorem in continuous time, a landmark result, was proven by Harrison and Kreps Secondly, the choice of the money market account as the unit by which we discount or rebase prices is unimportant.

We call the rebasing unit the numeraire. However, there is nothing special about the money market account. Any positive asset can be used as a numeraire. The intuition behind the fundamental theorem is that no-arbitrage is equivalent to the ratio of two assets remain- ing the same in risk-neutral expected value terms over time—loosely speaking, one asset cannot on average grow faster than another. Provided we have two linearly independent assets for example, the ZCB and the stock then we can eliminate risk at each step of the binomial tree, and risk-neutral and martingale arguments apply.

We restate a more general version of the fundamental theorem, which we do not prove here. In other words, the null sets of both probability distributions are the same; such probability distributions are called equivalent distributions.

We explore the change of numeraire in the next section, and in the exercises. In general, however, r and hence MT will not be constant. We can navigate the complexity of random interest rates in an elegant manner by choosing an alternative numeraire, the ZCB with maturity T. This holds regard- less of whether interest rates are constant.

Note that this choice of numeraire depends upon T, the maturity of the derivative. This expression, again a discounted expected value, holds even if interest rates are random, and becomes especially useful when we consider interest rate options in Part IV, when interest rates certainly cannot be assumed to be constant.

Z t, T We have here derived the forward price for the stock simply using the fundamental theorem, without making any assumptions about the risk-neutral distribution or whether interest rates are constant. We had to be able to accomplish this, since we earlier derived the forward price directly from the current stock and ZCB prices without making any assump- tions about its distribution, or even about possible values for the stock price.

It is reassuring that the two approaches the link being the proof of the fundamental theorem come up with the same result. We also have now, for the first time, identified the forward price as an expected value, in particular the expected value of the stock price under the risk-neutral distribution with respect to the zero coupon bond numeraire.

We present the following worked example. Recall the tree in Figure 8. We now change to the stock numeraire. We found the probabilities by invoking martingale conditions. Prices of derivative contracts are the same under either pair of numeraire and risk-neutral probability. The only facts we used about the real world probabilities of the up and down states are that only two states of the world are possible at each node, and that both states have non-zero probability.

Z t, T Z T, T Previously we determined the risk-neutral distribution uniquely from the possible states of the world on the binomial tree. We assume here without proof that an analogous pro- cess can be followed in continuous time. Whilst we immediately note that this allows non-zero probability of negative stock prices, let us assume for the moment that this probability is negligibly small and that the normal distribution is a reasonable approximation to the risk- neutral distribution.

In practice, approximate approaches like this can often be useful. Using put-call parity, it is straightforward to obtain put and straddle prices. This is an appealing result, and is often the point where derivatives professionals start their careers. On my first day in finance, I calculated an expected value then multiplied it by a discount factor. At the time it seemed a plausible approach to pricing derivatives, but in order to establish the result rigorously we needed the fundamental theorem.

In the past two chapters on replication, risk-neutrality and martingales, we have been exploring rich areas of derivatives pricing theory. We showed that options can be replic- ated by a portfolio of stock and bond, and that the replication price equals that given by discounted risk-neutral expectation.

These two elements form the heart of quantitative fin- ance. We showed the assumption of no-arbitrage is equivalent to the ratios of asset prices to the numeraire being martingales under the risk-neutral distribution.

In particular, derivat- ive prices can be calculated by taking discounted expected values of the derivative payout at maturity. We proved this for the binomial tree, and showed how we can change numeraire and the associated risk-neutral distribution.

In the next chapter we take the limit of the tree using the central limit theorem, and bridge to continuous time. It is often more elegant to work in continuous time where the manip- ulation of distributions and the calculation of the expected value of payouts is easier.

We do not prove the fundamental theorem in continuous time. Instead we repeatedly appeal to the binomial tree proof and the intuition it provides, and assume that key results carry over to the continuous case.

In particular, we do not concern ourselves with the mathematical conditions required to prove the fundamental theorem in continuous time. These condi- tions are almost always satisfied in the practical world, which is effectively discrete in time and value—for example, asset prices are only quoted to a finite number of decimal places.

Binomial tree: change of numeraire Consider a one-step, two-state world where a stock has current price After one year the stock is worth with probability 0. In particular, can the risk- neutral probabilities with respect to the ZCB and money market account ever differ?

Verify the answers are the same. Binomial tree: random interest rates I Consider the two-step binomial tree in Chapter 8 Question 1. Does the joint tree for Sm , Mm recombine? Do you want to revisit your comments in Question 1 b? Binomial tree: random interest rates II A stock that pays no dividends has current price Remember we are now working with a GBP asset so think of one dollar as a stock with price in pounds sterling.

Call price as numeraire A stock that pays no dividends has current price S0. The stock. The one-year strike European call. A forward contract with delivery price 90 and maturity one year. The one-year strike European put. Martingales and trading strategies Your answer should comprise fewer lines than the statement of the question.

In other words, you cannot beat the system. That is, a group cannot beat the system. What strategy can two traders in collusion implement to ensure that between them they get paid, even if X is a martingale? How does the presence of a stop-loss affect this strategy?

We investigate two particular limiting cases which give rise to lognormal distributions for the stock price ST , first under the real world probabilities and secondly in the risk-neutral case. This assumption turns out to be unimportant to the results but makes the arithmetic neater. We will take limits under the con- straint that the mean and variance of YT stay fixed as we increase the number of time steps N.

In particular, u and d will depend on T as we change the step size, although we will suppress this dependence in notation. Therefore, ST is lognormally distributed in this limiting case. The adjustment to obtain the risk-neutral probabilities would change accordingly. Note This is the most important tail integral in finance, and I believe everyone should do it at least once.

Revisiting it every couple of years after starting work on Wall Street is also a good way of keeping technically fresh. Note Observe how the Black—Scholes formula, a continuous-time result, has a similar form to the discrete-time Cox Ross Rubinstein formula obtained in Chapter 8.

The formula is named after Fischer Black and Myron Scholes who, along with Robert Merton, were pioneers of continuous-time finance in the s. Black died in — there was a sense of sadness and respect among options traders that day—but Scholes and Merton went on to win the Nobel prize in economic sciences in for their work on option pricing.

We obtained the Black—Scholes formula by calculating an expected value, drawing on the fundamental theorem of asset pricing. This route via martingales and expected values is particularly appealing to probabilists.

The original derivation in Black and Scholes is significantly different, and we outline alternative approaches to deriving the formula using stochastic processes, Ito calculus and partial differential equations in Chapter The Black—Scholes formula is one element of quantitative finance that has penet- rated broader public awareness, featuring in general interest news as derivatives received heightened scrutiny during the financial crisis.

In our exposition the formula has a straight- forward interpretation as the expected value of the option payout under the lognormal risk-neutral distribution. The formula enables one to translate between a particular under- lying dynamic for the asset—the limit of the binomial tree—and a unique arbitrage-free option price.

Whilst plausible, there is of course no reason why in practice the risk-neutral distribution should be lognormal. In Chapter 11 we explore the key duality between option prices and probability distributions, and show that the Black—Scholes formula can still be a useful tool even when lognormality does not hold. Figure The same result holds for d2. As the volatility of the stock tends to zero, the stock price becomes deterministic, equi- valent to a holding of cash invested at rate r.

If the stock is in-the-money-forward, then the call option becomes equivalent to a long forward contract. If it is out-of-the-money-forward, the call option is worthless. Our results show that these upper and lower bounds are in fact tight and cannot be improved, since we have presented cases where the call price becomes arbitrarily close to the bounds.

We can also derive a good approximation for the at-the-money-forward straddle price under Black—Scholes. This is one pragmatic method practitioners use to switch between approximately equivalent normal and lognormal distributions, both of which are often utilized in practice as reasonable candidates for the risk-neutral distribution. This is the basis for deriving the Black— Scholes formula via partial differential equations, which we sketch briefly in Chapter The vega of a call, put or a straddle is positive.

The holder of a straddle, for example, would want volatility to go up. We intro- duce, therefore, the concept of trading volatility, buying a straddle if one believes volatility is likely to increase. The vega of a forward contract, swap and FRA are all zero, since their value can be determined simply from the current prices of the stock or ZCBs. However, as we noted in Chapter 5, the vega of a future is not zero.

It will be positive if the underlying asset is pos- itively correlated with interest rates, since the convexity correction is proportional to the covariance. A long Eurodollar position, for example, is a short vega position. We know the vega of a long call position is positive, and that of a short call is negative, but what about the vega of a call spread, digital or butterfly? Intuitively, a contract is long vega if one would profit if volatility were to increase, and the stock be more likely to move more.

The precise point at which the vega is zero will depend on the option pricing model. Question 7 in the exercises explores the vega profiles of several option structures. Working with the stock and interest rate or ZCB separately, when both are random, can often be challenging. Use the fundamental theorem to calculate the price of a power call under the Black— Scholes model. You may use any result from Question 1. Capped power calls were briefly popular in derivative markets in the mids.

By comparing the payout functions of the capped power call with linear combinations of calls, find upper and lower bounds for the price of the capped power call in terms of the four call prices. Is there a least expensive upper bound and a most expensive lower bound? If so, find them. What is wrong with this argument? We will investigate two others. Vega and delta For each of the following positions I-X in Table Table The Black—Scholes formula by change of numeraire Let St be the price at time t of a stock that pays no dividends.

Which linear combination of i and ii gives the payout of a call option? Hence derive immediately the Black—Scholes equation for the price of a call option. In Chapter 7 we saw that the call option price did depend on the possible future states for the stock and hence its risk-neutral distribution.

Here we derive the result that option prices in fact determine entirely the risk-neutral distribution of ST. We can also price the digital option directly via the fundamental theorem. Z t, T Z T, T The price of the digital is thus simply the present value of the probability of receiving a payout, namely the stock price being above K at T.

This has to be positive as we require for a density function due to the convexity of call prices. This butterfly has payout at maturity T shown in Figure Therefore, by trading butterflies we are trading probab- ility, in particular the risk-neutral probabilities of possible states of the random variable ST.

Knowledge of call prices with maturity T determines the risk-neutral distribution at T. Note Under the lognormal risk-neutral distribution, call prices are given by the Black— Scholes formula. We leave it as an exercise to verify that differentiating the Black— Scholes formula twice does indeed reproduce the lognormal density function.

Forwards are as far one can go in developing pricing machinery without any distributional assumptions. Call options, on the other hand, tell us everything about the risk-neutral distribution at T. Elegant work in stochastic processes by Dupire and Derman and Kani gives conditions for when such information does indeed determine the stochastic process for St.

The notion of calls as a spanning set can be seen in a variety of ways. We can picture how we might replicate any arbitrary payout g ST at time T with a portfolio of calls. This is known as the implied volatility. Implied volatilities are calculated numerically as there is no analytic solution to the inverse of the formula.

In practice, implied volatilities for observed option prices of the same maturity but dif- ferent strikes are usually different. There can, of course, only be one risk-neutral distribution for ST. Rather, different implied volatilities are a manifestation that the risk-neutral distribution for ST is not lognormal. If it were lognormal, one volatility would determine option prices for all strikes. The first two terms give the price of what simple portfolio that approximates the derivative payout?

Power call spanned by calls Use Question 1 b to express the price of the power call Chapter 10 Question 3 as an integral of call prices. In the next few chapters, we introduce a range of widely traded interest rate derivatives, starting with European options on libor rates and swaps, known as caps, floors and swaptions. That is, a caplet is a call on a libor rate.

Why is it called a caplet? If one assumes LT is lognormally distributed, then one obtains the Black formula. The cap market—which is deep and liquid—adopted this formula for years, but a rigorous proof that this formula was not internally inconsistent did not come until two decades later, in the work of Miltersen et al. This formulation provides something else of importance. We briefly sketch how one might change from one probability distribution to another in continuous time in Chapter A cap is a portfolio of consecutive caplets.

The structure of a cap is shown in Figure That is, a floorlet is a put on a libor rate. But we can apply a similar elegant technique as used in caplet valuation. An appropriate choice of numeraire allows us to work directly with the distribution of the swap rate yT0 [T0 , Tn ], conditional on yt [T0 , Tn ]. This allows us to take the pv01 term out of the expectation and to deal with the random variable yT0 [T0 , Tn ] analogously to LT.

A payer swaption, struck at K with expiry T on a swap from T to Tn , is the option to pay fixed K and receive libor on the swap. This is called a T into Tn — T payer swaption. We display a swaption graphically in Figure A receiver swaption struck at K is the option to receive fixed K and pay libor on the swap. A swaption straddle is a payer and a receiver swaption of the same strike and dates. A payer swaption can be thought of heuristically as a call on a swap rate, multiplied by the pv01 term PT [T, Tn ].

Note Here, the exercise date and start date of the swap coincide. This holds for the vast majority of swaptions traded in the market, although does not have to be the case. These are called midcurve swaptions. We will apply a similar approach to valuation. This is called the swap numeraire. Once again, yt [T, Tn ] is itself a ratio of assets to the numeraire, so must itself be a martin- gale under the risk-neutral distribution. As mentioned in Chapter 11, there is no reason why the risk-neutral distribution for the swap rate or libor need be lognormal.

Similar to the Black—Scholes formula, the Black formula is a one-to-one function between volatility and option price. The presence of a volatility skew would indicate that the risk-neutral distribution is not lognormal. Note The simple notation T for the expiration does not capture the vital importance of the exact expiration date and time for a swaption trader. Throughout the s, most swaptions were exercised by voice, meaning the owner of the swaption would need to call the seller of the swaption to inform them of exercise.

Rare errors would typically be resolved between bank management, as both sides knew the situation could be reversed at some point in the future. Black formula Derive the Black formula. For what values of K does the digital caplet have zero vega, for I and II respectively?

Explain your answers in terms of the median of lognormal and normal distribu- tions. Cancellable swaps can be European style with just one cancellation date, Bermudan style with multiple cancellation dates, or American style with continuous cancellation dates which in practice usually means daily. We here outline the construction of cancellable swaps using swaptions, and explore several features of Bermudan swaptions.

That is, if we cancel the swap at Tj , no subsequent swap payments are made and thus the value at Tj is trivially zero. We can deconstruct the cancellable swap into a vanilla swap with fixed rate K from T to Tn , plus a Tj into Tn — Tj receiver swaption with strike K.

The option to cancel the swap is precisely achieved by exercising the receiver swaption, which exactly offsets the swap from Tj to Tn. The cancellable swap can also be deconstructed into a swap with fixed rate K from T to Tj , plus a Tj into Tn — Tj payer swaption with strike K.

The equivalence of these two constructs, which are shown in Figure The following question naturally arises. Using our second deconstruction, the value of the cancellable swap is the sum of the value of the swap from T to Tj and the price of the Tj into Tn — Tj payer swaption. It might be the case, for example, that investors prefer fixed rate bonds to floating rate bonds, but the corporate issuer prefers floating rate liabilities.

By swapping a fixed rate bond as shown in Figure The swap rate, however, is essentially independent of the credit of the issuer.

In a similar manner to above, the company often will exchange these fixed payments for libor payments using a cancellable swap, as shown in Figure The swap counterparty now has the right to cancel the swap at Tj. Typically, the issuer will automatically call the bond if the swap is cancelled. Indeed, why are callable bonds such a popular instrument both for issuers and investors? The former incorporates investor preference for the two different types of bond, whilst the latter is based on the market price for swaptions.

Whilst investors may often want a bond with a higher coupon and so are attracted to the callable version, they may not have properly assessed the extra coupon they should receive for selling the cancellation option. Note The optics of a callable bond can appear attractive to investors. For example, suppose a company can issue a two-year bond with a coupon of 5.

The investor might conclude that the callable bond is attractive, since the investor beats the two-year rate 5. However, if rates go down sufficiently for the bond to be called after two years, the investor receives 5. The investor thus bears significant reinvestment risk with the callable bond.

In practice, it might be that the two-year swap rate is 4. Bermudans have an appealing combination of being easy to define, and yet possessing unexpected dimensions of subtlety. Pricing Bermudans in all their complexity is a rich field beyond our scope and still the subject of current research. In this book we develop a broad range of arbitrage bounds and model-independent results for Bermudans, which we can derive without advanced option pricing machinery.

Let us first recap interest rate derivatives we have encountered so far. A swap is an exchange of cashflows where one counterparty pays a fixed rate K and receives libor each period from T0 to Tn.

The libor rates referenced by a T0 by Tn cap are the same as those referenced by a T0 into Tn — T0 swaption. For example, a two-year into three-year 2yr-into-3yr swaption references the same libor rates as a two-year by five-year 2yr-by-5yr cap.

The relative value between these instruments forms a significant component of the interest rate derivative trading landscape. If the swaption is not exercised at Ti , then the option continues. Once the option is exercised at a particular Ti , all subsequent options disappear. That is, there are many exercise dates but only one option.

We now establish a series of bounds on the price of the Bermudan in terms of European- style interest rate options. In other words, we assume the cap is on three-month libor, and that all swaps have quarterly payments on the fixed side versus three-month libor quarterly payments on the floating side. In practice, the frequency of the various options may vary. Proof To prove an inequality, we assume it does not hold, and show that we can then construct an arbitrage portfolio.

For example, we prove the second inequality in a as follows. Then we can sell the Tj into Tn — Tj European payer swaption and buy the Bermudan swaption, receiving a positive amount of cash. Equivalently the portfolio consisting of short one European swaption, long one Bermudan swaption and a positive holding of cash has zero value at time t. If the European is not exercised at time Tj , we do not exercise the Bermudan.

We are left with a positive amount of cash. If the European is exercised at time Tj , we exer- cise the Bermudan at time Tj , setting up two exactly offsetting swaps. Once again, the portfolio is left with a positive amount of cash. Hence we have created an arbitrage portfolio.

Note In during the aftermath of the Lehman Brothers bankruptcy, Bermudan receiver swaptions traded at a higher price than libor floors of the same strike and underlying dates. This meant that the elementary arbitrage bounds on Bermudan swaption prices developed here and in Question 2 a were violated. Whilst the arbitrage bound violation lasted only a few days, it did nevertheless provide a caution- ary note regarding the foundations of derivative pricing. See Blyth for further discussion.

Therefore, the exact exercise condition at time Ti , as shown in Figure This is of limited use since we do not yet have a way of valuing the subsequent Bermudan option. In practice, we would attempt to build a tree for the evolution of interest rates and work backwards through the tree, in a similar manner to how we priced the American put on a stock on the binomial tree see Question 1 in Chapter 8. However, we can make progress by considering model-independent exercise criteria, which depend only upon swap rates and European swaption prices observed at the exer- cise date.

Param Jeet has been into the analytics industry for the last few years and has worked with various leading multinational companies as well as consulted few of companies as a data scientist. Prashant has been into analytics industry for more than 10 years and has worked with various leading multinational companies as well as consulted few of companies as data scientist across several domain.

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Learning Quantitative Finance with R. Download e-Book. Posted on. Contact Us. Upload eBook. Privacy Policy. New eBooks. Search Engine. Introduction to R for Quantitative Finance. R is a statistical computing language that's ideal for answering quantitative finance questions.

This book gives you both theory and practice, all in clear language with stacks of real-world examples. Ideal for R beginners or expert alike.

Overview Use time series analysis to model and forecast house prices Estimate the term structure of interest rates using prices of government bonds Detect systemically important financial institutions by employing financial network analysis In Detail Introduction to R for Quantitative Finance will show you how to solve real-world quantitative finance problems using the statistical computing language R.

The book covers diverse topics ranging from time series analysis to financial networks. Each chapter briefly presents the theory behind specific concepts and deals with solving a diverse range of problems using R with the help of practical examples. This book will be your guide on how to use and master R in order to solve real-world quantitative finance problems.