MC simulation & Time-Dependent Parameters

Quintenk · June 28th, 2011, 2:50 pm

In most (introduction) books on derivatives pricing the risk-free interest rate/dividend yield is assumed to be constant over time when performing Monte Carlo simulation.For valuing path-dependent options it seems to be more "correct" to relax this assumption and to make use of rates/yields which are a deterministic function of time.My guess is that I should make use of the respective forward rates/yields.Can someone confirm this understanding (and provide a reference where this discussed further in detail)?

bwarren · June 28th, 2011, 11:28 pm

Yes you can incorporate dynamic interest rates into the model. One option is to use the deterministic forward rate curve.

speedBoots · June 30th, 2011, 2:23 pm

bwarren's idea is probably best but you can also simulate the short rate. So if, for example you wanted a 3M rate at each point, you could fit a model to do this. Let me know if you would like matlab code for parameter estimation.

bwarren · July 1st, 2011, 9:39 pm

Yes but if you're derivative isn't that sensitive to interest rates, it could be overkill. Monte carlo can be expensive.

Quintenk · July 4th, 2011, 8:18 am

Thanks for your replies. Since the derivatives I need to price are equity derivatives I also think that doing a short rate model is overkill. In the mean time I have also found a section in "Monte Carlo Methods in Financial Engineering " by Paul Glasserman (2004) on "Incorporating a Term Structure" (p. 101) which basically answers my question.

ZhuLiAn · July 4th, 2011, 8:44 am

You can have interest rate risks if your options have long maturities otherwise it's should be small. What you could do maybe using the equations in Glasserman is trying different interest rate curve shapes and see if there is any impact on your product.