My understanding of the relationship between stock option pricing and interest rates is that rates affect option values due to the cost of carrying a hedged portfolio; leading to a positive relationship between rates and calls, and inverse relationship between rates and puts. Am I thinking of this correctly?
Also, if my earlier statement holds true, then why do we discount the payoff with binomial model valuation by the risk-free rate for both calls and puts?
Any and all help is appreciated.
Not sure about your logic on “hedged” portfolio… what are you hedging?
You are correct that call options are positively related to interest rates, while put options are negatively related? Why? Because in a call, you can invest the money that you didn’t have to use when you brought the call, rather than buying the asset outright. It’s also spelled out in BSM, Binomial, and put call parity ==> p + s = c + x
The binomial’s hedge factor is opposite signs for calls and puts == > C0 = hS0 + (-hS+ + C+)/(1+R)
Also, the change in the interest rate in not only changes how you discount the put/call values in each period, but also changes the up/down probability and will reflect the relationship mentioned above.
I think it was the changes in “Risk-neutral probability” due to the change in interest rates that I was neglecting. Thanks for chiming in.