Now lets look more carefully at very-low-strike puts. Suppose theres a threshold strike, call it K₁, 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 K₁ the put price formula should be:

PUT PRICE = e^-r(T-t) x (K - $1) x (PROBABILITY OF BANKRUPTCY)

v libri (Bo... 14 ~ A Aa v Po A (A) Uab X, X ADA A . Paragraph Styles Dictate Sensitiv PUT PRICE (6-MONTH EXPIRY) vs STRIKE $18 $16 $14 $12 $10 $8 $6 $4 $2 $0 $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 4. 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. 3 83 of 2238 words Focus 21 v libri (Bo... 14 ~ A Aa v Po A (A) Uab X, X ADA A . Paragraph Styles Dictate Sensitiv PUT PRICE (6-MONTH EXPIRY) vs STRIKE $18 $16 $14 $12 $10 $8 $6 $4 $2 $0 $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 4. 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. 3 83 of 2238 words Focus 21