In: Finance
Consider a portfolio that consists of buying a call option on a stock and selling a put option. The stock pays continuous dividends at the yield rate of 5%. The options have a strike of $62 and expire in six months. The current stock price is $60 and the continuously compounded risk-free interest rate is 15%. Find the elasticity of this portfolio.
The Delta of the portfolio
= DELTA of Call option (62) - DELTA of Put option (62)
= exp(-delta*t) = exp(-0.05*0.5) = 0.97531
Value of the portfolio
= Call option (62) - Put option (62)
= Stock *exp(-delta*t) - K*exp(-r*t)
= 60*exp(-0.05*0.5) - 62*exp(-0.15*0.5) = 0.9985
Thus, the elasticity of the portfolio is:
(DELTA of the portfolio)*Stock /(Value of the portfolio) =
0.97531*60/0.9985 = 58.606