You buy a share of stock, write a 1-year call option with X = $55, and buy a 1-year put option with X = $55. Your net outlay to establish the entire portfolio is $54. The stock pays no dividends. a. What is the payoff of your portfolio?

Question

Business

Terminator

10 August, 08:07

You buy a share of stock, write a 1-year call option with X = $55, and buy a 1-year put option with X = $55. Your net outlay to establish the entire portfolio is $54. The stock pays no dividends. a. What is the payoff of your portfolio?

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Brian Russo · Answer 1

0.0185 or 1.85%

Explanation:

The payoff table shows that the portfolio is riskless with time-T value equal to $55.

Position

ST < 55

ST > 55

Buy stock: ST, ST

Short call: 0, - (ST - 55)

Long put: (55 - ST), 0

Total: 55, 55

The risk-free rate is: ($55/$54) - 1 = 0.0185

=1.85%

Therefore the payoff of the portfolio is $1.85%