Derivatives Dependent on a single Underlying Variable Consider a variable, 0, (not necessarily the price of a traded security) that follows the process d e S Imagine two derivative s dependent on e with prices f, and f2. Suppose

Models to be Considered Constant elasticity of variance (CEV) Jump diffusion Stochastic volatility Implied volatility function (IVF) Options, Futures, and Other Derivatives

Binary options Nonstandard American Lookback options options Shout options Forward start options Asian options Compound options Options to exchange Chooser options one asset for another Barrier options Options involving

Binomial trees are frequently used to approximate the movements in the price of a stock or other asset In each small interval of time the stock price is assumed to move up by a proportional amount u or to move down by a proportional amount d Options

Standard approach to Estimating Volatility Define on as the volatility per day between day n-1 and day n, as estimated at end of day Define S: as the value of market variable at end of day i

What loss level is such that we are y%o confident it will not be exceeded in n business days?

Put-call parity p +spe-ql=c+Xer holds regardless of the assumptions made about the stock price distribution It follows that

A bank has sold for $300,000 a European call option on 100,000 shares of a nondividend paying stock S=49,K=50,=5%,=20% T=20 weeks,μ=13%

European Options on Stocks 13.2 Providing a dividend yield We get the same probability distribution for the stock price at time T in each of the following cases 1. The stock starts at price so and provides a dividend yield =q 2. The stock starts at price Soe q l and provides no income

The Stock Price Assumption Consider a stock whose price is s In a short period of time of length 8t, the return on the stock is normally distributed