Does it assume constant volatility? why?
Yes - have to assume constant vol…one of the method shortcomings. Vol 5 pg 251 “Two problems with using implied vol…Second, option pricing models assume that volatility is constant over the life of the option. Therefore interpreting becomes difficult”
implied vol is one number, therefore it must be constant
The constant volatility is one of the assumption in BSM model from which you can derive value of options using volatility, rfr, time. Implied volatility is derived from model by putting market price in the model and deriving a value for volatility from a formula which is like ‘implied by the market’.
The assumptions underlying the BSM model are: - The price of the underlying asset follows a lognormal distribution. - The (continuous) risk-free rate is constant and known. - The volatility of the underlying asset is constant and known. Option values depend on the volatility of the price of the underlying asset or interest rate. - Markets are “frictionless.” There are no taxes, no transactions costs, and no restrictions on short sales or the use of short-sale proceeds. - The underlying asset has no cash flow, such as dividends or coupon payments. - The options valued are European options
Defo constant volatility. It’s the volatility implied by the market price. How do you get multiple volatilities out of one single equation??
constant volatility