Question

On March 5, 2018 you purchased an option which will allow you to sell a commercial...

  1. On March 5, 2018 you purchased an option which will allow you to sell a commercial building on September 20, 2024 for $30 million. Your current estimate of the value of the commercial building is $32 million. The annual volatility for the change in the commercial building’s value is 45% and the risk-free rate is 7%.
    1. What type of option is this?
    2. Calculate the value of the option to sell the commercial building.
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Answer #1

Given: Spot price of building = $32 million, Future price of building = $30 million, Annual volatility = 45% and Risk free rate = 7%.

a) This a European put option, because this is giving you rights to exercise your option on the expiry only.

b) The price of this put option is the premium + intrinsic value of commodity.

Intrinsic value of commodity = cost of carry of this option = $30 million X e^-rT = $30 million X 2.71828^(-0.07X6.54)

=> $30 million X 2.71828^(-0.4578) = $30 million X 0.63 = $18.98 million.

Premium = Will be the market premium.

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