Standard Approach to Estimating Volatility (Equation 15.1 Define on as the volatility per day between day n-1 and day n, as estimated at end of day n-1 · Define, as the value of market variable at end of day i Define ui= In(S /Si-1)
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?
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
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
Types of Rates Treasury rates(国债利率)—regarded as risk-free rates LIBOR rates (London Interbank Offer rate)(伦敦银行同业放款利率)-generally higher than Treasury zero rates Repo rates(回购利率)—slightly higher than the Treasury rates
Futures Contracts Available on a wide range of underlyings · Exchange traded · Specifications(规定) need to be defined: -What can be delivered, Where it can be delivered,& When it can be delivered Settled(结算) daily
