Consider a portfolio that consists of buying a call option on a stock and selling a...

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.

Solutions

Expert Solution

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

jeff jeffy answered 2 years ago

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