[PROBLEM C] PUT PRICE (6-MONTH EXPIRY) vs STRIKE 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 PUT PRICE @ 22% IV PUT PRICE @ 40% IV This problem references the same set-up as in [PROBLEM B]. Current stock price for XYZ | $50.00 Interest rate 3% Dividend rate 0% The graph shows the price profile (in the Black-Scholes model) of 6-month options on XYZ (across the "strike domain") for two different implied volatilities (IVS): 22% and 40%. Recall that 22% is the implied volatility where the $50-strike put was priced and 40% is the implied volatility where the $30-strike put was priced. [1] Can you locate on the graph the price ($2.74) of the $50-strike put and the price ($0.14) of the $30-strike put? [2] At what strike level is the price difference (for the two different implied volatilities) the biggest? Any thoughts on this? [EXTRA CREDIT] For a fixed implied volatility we see that as we go lower in strike the put price drops ... but at a slower and slower rate. Any ideas on why this is happening? Hint: Recall that the put price can be written using an integral of the option payoff MAX(K-S(T), 0 times the probability density function (pdf) of S(T). What does the model assume about the shape of this pdf? [EXTRA CREDIT] Now ... let's look more carefully at very low-strike puts. Suppose there's a "threshold strike," call it K, for which the only way that XYZ could fall below K1 over the next 6 months is if the company went bankrupt over the period. And assume that if that were to happen the stock price would fall to $1. Show that for any strike k