Answer to Question #175725 in Financial Math for Andrea

Question

XYZ’s stock price in $100. 1-year European-style options on XYZ are trading at an implied volatility of 15%. (Assume zero dividends and zero interest rates: q=0% and r=0%.) 

 

[a] Where should we set the strike price of a 1-year call to give it a delta of +0.25?   

 

[b] q=0% and r=0% imply that the forward price = $100. It follows from put-call parity that $100-strike call and the $100-strike put are priced equally. Are their deltas +0.50 and -0.50, respectively?

Answer 1

a) Since q=0% and r=0% ,the formula for Black Scholes delta formula is

0.25 = N[ ln(100/k)/0.15 +0.075]

From tables

N[0.66] =0.25

0.66 = ln(100/k)/0.15 + 0.075

0.08775 = ln (100/k)

exp( 0.08775) = 100/k

k =91.60

b) Given q=0% and r=0%

Considering put call parity

C_t+P_t = S_t+K. exp^(rt)

100 -100 = 100- 100

Hence it holds and hence overall delta is equal to zero