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# Noob question about interest rates and options?

Discussion in 'Options' started by larryg003, Aug 20, 2010.

1. ### larryg003

I've been reading Natenberg's book 'Options as a Strategic Investment'
and was wondering several things.

On pg. 48, he says

"If the underlying contract is subject to stock-type settlement, as we raise interest rates, we raise the forward price, increasing the value of calls and decreasing the value of puts. Secondly, the interest rate may affect the cost of carrying the option. If the option is subject to stock-type settlement, as we raise interest rates we decreased the value of the option. In spite of the fact that the interest rate plays two roles, in most cases the same rate is applicable and we need only input one interest rate into the model. If, however, different rates are applicable, such as would be the case with foreign currency options (the foreign currency interest rate plays one role, the domestic currency interest rate plays a different role) the model will require the input of two interest rates. This is the case with Garman-Kohlhagen version of the Black-Scholes Model."

Can someone explain this paragraph to me?

1.) Why does the forward price increase as the interest rate increases? Why does the value of calls increase and price of puts decrease?

2.) If the interest rate affects the carrying cost of the option, why does it decrease the values of options?

Thank you for all of you help,

-Larry

2. ### spindr0

Consider a conversion profit formula:

conv = strike - stock + call -put - carry + div

Assume stock at strike, no div and fair pricing then:

call = put + carry

If the carry cost increases, the difference b/t the p&c increases, the bump being split b/t them. IOW, if the carry cost increases 10 cts, the put is priced 5 cts lower and the call is priced 5 cts higher.

3. ### MTE

1. The forward price has two components - spot price and cost of carry (cost of carry consists of carrying costs less any income received by holding the underlying asset). When you enter into a forward contract to buy some stock at a future date then essentially you are postponing the payment for the stock and thus can invest the cash you would've otherwise used to buy the stock in a risk free asset. The person on the other side is in exactly the opposite position, by postponing the sale of the stock he/she doesn't receive the cash, which could've been invested in a risk free asset. The higer the risk free interest rate the higher the income hence the higher the cost of carry.

The same reasoning applies to options. A call option allows you to postpone the purchase of the stock and thus collect interest on a risk free asset. While the put option postpones the sale of the stock and thus you forgo the risk free interest.

2. The higher the interest rate the higher the value of the call and the lower the value of the put. However, there is also a secondary cost of carry, the one that applies to actually purchasing the option (i.e. the money you spend on the premium), but it's not really big enough to make that much of a difference, especially in a current ultra low interest rate environment.

Proper definition of carry includes dividend. Interest cost would have been a better term.

5. ### spindr0

It always amuses me how wrong all the option authors are and how right you think you are