Help with derivatives problem

[BDP]

Can someone help me figure out the answer to this question:

1. European Call Options on Horses. You are raising what you think to be an exceptional show horse, a Filly named Santana’s Cinnamon Girl. Miss Donna really wants to buy this horse from you today. She has dangled a tempting offer in front of you, $60K (and she pays the Creech Brothers to haul the filly). You think that offer is the correct price today for this filly. But, you are thinking, “This filly could really be something, and turn out to be worth $122K. By selling it today, I really could be losing out. On the other hand, this filly is a tad “Wild,” and might only be worth $10K in one year.” You both think these cases are equally likely, hence you both think the price today of $60K is fair. You and Miss Donna agree that the appropriate equine interest rate for one year is 10%. After reading about European call options on www.areoptionsreallyforyou.com (http://www.areoptionsreallyforyou.com), you realize that you could sell Miss Donna an option today that would allow her to buy Cinnamon Girl in one year for $60K.

First, compute the price of this call option. Then, for insurance purposes, how much would you be willing to pay today to insure the filly for $60K?

what's throwing me off is the fact that the strike prices for the options are not given so I can't calucate anything else. please help!


Thanks!

[sizeup]

BDP,

The strike prices of the options are given: the call option is to buy at 60k and the put option is to insure at 60k, so the strikes are both 60k.

Traditional option pricing theory relies on a volatility of the underlying. In this case we can use your distribution of values for the horse in 1 year instead: 50% chance it's worth 122,000 and 50% chance it's worth 10,000.

From that, the option to buy the horse for 60,000 is fairly valued at: (0.50) x PV(122,000 - 60,000) = (0.50) x PV (62,000) in 1 year. The discount factor to calculate the present value of that 62,000 1 year from now back to today depends on your cost of funds, etc. so will be a little less than 31,000 today.

The put is similar: 50% chance it's worth 50,000 in a year (60,000 strike - 10,000 value on the downside) or a little less than 25,000 depending on how steeply you want to discount it.

Am not sure what you mean by "appropriate equine interest rate" but the discounting is more a function of your cost of funds, investment alternatives, and liquidity than something agreed upon with the buyer. The value of either option to you should be priced based on that and then you should build in an edge to capture your +EV. How much edge depends on your aggressiveness and your evaluation of what the market will bear!

-sizeup

[BDP]

Thanks!