Question

Given the following data on a weather option:

Option type: CALL
Underlying: Heating Degree Days
Contract period: Nov 1, 1999 – Mar 31, 2000
Met Office: Chicago/O’Hare Airport
Strike: 4500
Dollars per unit (Tick Size): $10,000
Maximal (Limit) payoff: $1,000,000
Write the expression for the payoff on the weather option
a. Payoff = min($10,000*max(4500 – Total HDD,0),$1,000,000)
b. Payoff = min($10,000*max(Total HDD – 4500,0),$1,000,000)
c. Payoff = max($10,000*min(Total HDD – 4500,0),$1,000,000)
d. Payoff = max($10,000*min(Total HDD – 4500,0),$1,000,000)

Answer 1

The correct expression for the payoff on the described call option on Heating Degree Days is 'min($10,000 × max(Total HDD – 4500, 0), $1,000,000)', which calculates the payoff based on the total HDD exceeding the strike value, up to a maximum payoff limit.

Step-by-step explanation:

The expression for the payoff on a weather option, specifically a call option on Heating Degree Days with a strike of 4500 and a tick size of $10,000, can be described as the minimum of the product of $10,000 and the maximum of the total Heating Degree Days minus the strike, and the maximal limit payoff. Since a call option profits when the underlying exceeds the strike, the proper expression for the payoff is: Payoff = min($10,000 × max(Total HDD – 4500, 0), $1,000,000)

This means that if the total Heating Degree Days are above the strike of 4500, the payoff will be $10,000 times the amount by which it exceeds the strike, up to a maximum of $1,000,000. If the total Heating Degree Days are below the strike, the payoff is $0, as the 'max' function would result in 0. The 'min' function then ensures the payoff doesn't exceed the capped amount of $1,000,000.