So I have this really tough homework question that I could really use some help with from out there;
Suppose you work for an investment bank and a client wishes to purchase a security that behaves like a long position on the futures contract on the 5-year Treasury bond with expiry in 3 months, except that he wishes to limit his downside exposure to falling futures prices. He is willing to forego some upside exposure in order for the security to have a value of zero. He does not wish to pay any money upfront.
a) (5 points) Briefly describe what combination of futures contracts and European options that will create the desired payoff profile for your client.
My answer: Long a call and short a put to create a long position on the futures security.
b) (5 points) Suppose now that the futures price on the 5-Year Treasury bond contract is 100. The volatility of the futures price is 20% and the risk free rate is 5%. The client specifies that he does not wish to incur losses beyond a futures price of 90. Using Black’s formula for options on futures contracts, compute the appropriate strike prices on the option contracts that ensure the value of this package of securities is zero. Hint: You should use the function NORMSDIST in EXCEL to compute Black’s formula and the “solver” tool in EXCEL to find the answer.
My answer: how the hell do you back out the strike price? and isn't the strike price mentioned? i.e 90$
If you short on put, if the future contract goes to 0 the counter party will exercise the option.You didn't limit his downside potential.
Correct answer on my opinion should be long one call option and long one put option. Since he don't want to pay anything. Let him borrow at risk-free rate.
Pay-Out: If future price goes up: Unlimited (Since stock price can go to...) - Loan = Unlimited
or Future Price = 0, The Strike Price for put option - 0 - Loan.
I realized later on that it should be long a put and short a call. I also sort of realized how to solve the question. He doesn't want to pay anything upfront but if he longs, he will have to pay two premiums.
You long the futures contract, but you don't pay anything upfront until expiry when you pay. You also long a put at strike 90 to get a put value of 0.3678. Remember he wants the total package value to be zero,
so value of put - value of call = 0, by using black-scholes we find value of put to be 0.3678 assuming strike price of 90 and the other conditions. Now we need to find the strike price of a call option such that it's value is 0.3678. This is the tricky part and it involves using a solver in excel which uses an iterative method to come up with a strike price. The strike price that you get from the iterative method is 116.81.
So in Essence the position you take is;
Long a futures option - only pay when you reach that point Long a put option at strike of 90 and value = 0.3678 Short a call option at strike of 116.81 and value = 0.3678
This way he limits his losses from falling prices due to the put and also if prices sky rocket to 200 thus leading the call to be in the money and him being the loser from writing the call, he is still long a futures contract which will protect him.
it would be great if someone could confirm my logic up there. thanks
Assuming you calculated the prices of the put and the call correctly, then you are right. The idea is to create a zero premium collar, which is what you did. Can you explain how you use Excel to find this? I usually just use the CBOE options calculator and then iterate by hand.
You need to use the solver function in excel to solve this. In the solver you put the target cell as the one that contains the final equation and the cell to be changed is the strike price. You don't need to set any other constraints in the equation.
Non aliquam eos assumenda neque at. Cupiditate aut eum illo omnis. Est ad et qui vel a velit itaque.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...