A Course in Financial CalculusFinance provides a dramatic example of the successful application of mathematics to the practical problem of pricing financial derivatives. This self-contained text is designed for first courses in financial calculus. Key concepts are introduced in the discrete time framework: proofs in the continuous-time world follow naturally. The second half of the book is devoted to financially sophisticated models and instruments. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts are applied to realistic financial questions. |
Contents
Brownian motion | 51 |
Stochastic calculus | 71 |
13 | 90 |
18 | 100 |
The BlackScholes model | 112 |
Different payoffs | 139 |
Bigger models | 159 |
| 189 | |
| 193 | |
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Common terms and phrases
American put option arbitrage B₁ Black-Scholes equation Black-Scholes model Black-Scholes price calculate Chapter claim continuous defined Definition denote derivative discounted asset price discounted stock price discrete dollar European call option European options Example Exercise expiry F₁ filtration forward contract function geometric Brownian motion Girsanov Theorem hedging portfolio implied volatility interest rate Itô Itô's formula jumps Lemma M₁ market models martingale measure Martingale Representation Theorem maturity measure Q multifactor notation numeraire obtain option with strike P-Brownian P-martingale partial differential equation payoff Poisson process portfolio consisting pricing and hedging pricing formula probability measure proof put option random variable replicating portfolio risk-free riskless cash bond risky asset S₁ self-financing solution solves standard Brownian motion Sterling stochastic differential equation stochastic process strategy strike price Suppose tradable asset units of stock V₁ vector W₁ write X₁ Z₁ zero дх