The Question Being Asked in Value at Risk (VaR) \What loss level is such that we are X% confident it will not be exceeded in N business days?\

Example AFI has SOLD for $300,000 a European call on 100,000 shares of a non-dividend paying stock: S 0 =49 =50 r=5%=20% μ=13% T =20 weeks The Black-Scholes value of the option is $240,000 How does the Fl hedge its risk?

European Options on Stock 12.2 Paying Continuous Dividends 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 continuous dividend yield q 2. The stock starts at price Soe-q' and provides no dividend yield

The stock Price Assumption Consider a stock whose price is s In a short period of time of length At the change in then stock price S is assumed to be normal with mean Sdt and standard deviation os√△, that is, S follows geometric Brownian motion ds=u Sdt+oSdz Then dInS=( )dt+oda

Categorization of Stochastic Processes 1 Discrete time; discrete variable 2 Discrete time; continuous variable 3 Continuous time; discrete variable 4 Continuous time; continuous variable Options, Futures, and Other Derivatives,4 4th edition2000 by John.hull Tang Yincai, 2003, Shanghai Normal University

A Simple Binomial Model of Stock Price Movements In a binomial model, the stock price at the BEGINNING of period can lead to only 2 stock prices at the END of that period

Three Alternative Strategies · Take position in: -the option and the underlying -2 or more options of the same type This is known as spread -a mixture of calls and puts This is known as a combination

Notation : European call C: American Call option option price price p: European put P: American Put option option price price So: Stock price today·Sr:Stock price at time X: Strike price D: Present value of T: Life of option

Assets Underlying Exchange-Traded Options Page 151-2 · Stocks · Foreign Currency · Stock Indices · Futures · Commodities etc

Nature of Swaps A swap is an agreement to exchange cash flows(现金流)at specified future times according to certain specified rules