Black scholes with continuous compounding interest

chinnu · May 12th, 2003, 1:31 am

Hi, I was trying to implement Black Scholes and I am using calculator provided in NumaWeb as reference; I am comparing my results with that calculator. WHen I use simple interest I am geeting same results as that calculator. But when I am using Continuous(CC) compound interest I am getting different results. What should I do to in the case of CC. What I did was replace Interest rate with CC rate ln(1+IR*T)/T is that correct? What modification should I make in order for my calculator to work.Thank youchinnu

WannaBeDude · May 12th, 2003, 11:31 am

Hello chinnu, Maybe taking a look at how the solution is derived will help you. Take a look at what kind of compounding is being used in the derivation.. You can follow this link... http://www.physics.uci.edu/~silverma/bseqn/bs.pdf Regards

mrbadguy · May 12th, 2003, 12:18 pm

Have a look to this short note on basics about compounding interest rates. Apologies for elementary explanations, maybe it helps. http://www.math.missouri.edu/~math5n10/ ... PPL.35.pdf

Aaron · May 12th, 2003, 9:57 pm

I think what you're doing is taking a simple interest rate and converting it to continuous compounding to use as an input to Black-Scholes. That's fine, you should do that in theory, but it shouldn't make much difference in practice unless interest rates are very high.However, Black-Scholes calculators always ask you to input the continuously compounded rate. So if you do your own calculation using the continuously compounded rate, but put the simple interest rate into the calculator, you will of course get different answers.

swapi · June 21st, 2005, 7:23 pm

Thank you Aaron I always apreciate your interventions. light;Do you know by any chance what rates to input in a FX black scholes option pricer? Libor, Depo? It seems that some even use the market FX forward price and deduct the domestic rate.

Aaron · June 22nd, 2005, 1:46 am

For equities and most commodities, with stable currencies, it shouldn't make much difference. In theory, there should only be one riskless rate. I think the swap rate is probably the best one to use, but Libor or implied forward or treasuries aren't bad either. Some people try to use the average of their borrowing and lending rates, which makes sense for highly-rated institutions, but not for others.