What option pricing biases are likely to be observed when

UCL Volatility Smile Case Study Questions

Study Questions – Volatility Smile

 1. What option pricing biases are likely to be observed when:

a. Both tails of the stock price distribution are thinner than those of the lognormal distribution?

b. The right tail is thinner, and the left tail is fatter, than that of a lognormal distribution?

2. What biases are caused by an uncertain volatility when the stock price is positively correlated with volatility?

3. What biases are caused by jumps in the movements of a stock price? Are these biases likely to be more pronounced for a six-month option than for a three-month option?

4. Why are the biases (relative to the Black-Scholes) for the market prices of in-themoney call options usually the same as the biases for the market prices of out-of-themoney put options?

5. Suppose the stock price follows a stochastic volatility model with the stock price and its volatility positively correlated. The Black-Scholes model is used to calculate implied volatilities for call and put options with different exercises prices and time to maturity. What patterns would you expect to observe in the implied volatilities?