$18 $16 $14 $12 $10 $8 $6 $4 PUT PRICE (6-MONTH EXPIRY) vs STRIKE $2 $0 30 31 32 33 34 35 36 37 38 39 4041424344454647484950515253545556575859606162636465 PUT PRICE @ 22% IV -PUT PRICE @ 40% IV Current stock price for XYZ = $50 Interest rate = 3% Dividend rate = 0% The graph shows the price profile (option price vs strike, Black-Scholes model) of 6-month options on XYZ, for two different implied volatilities (IVS): 22% and 40%. 22% is the implied volatility where the $50-strike put is priced and 40% is the implied volatility where the $30 strike put was priced a) Looking at the graph. For each fixed implied volatility, as it goes lower in strike the put price drops but at a slower and slower rate. Any ideas on why this is happening? Note: The put price can be obtained as the present value of the expected option payoff under the density function for S(T): exp(r(T t)) [(K u) pdf (u) du where the integral is from 0 to K. What does the model assume about the shape of this pdf?