Say that I have a continuous forward rate for each year from 1 to 10 years and I am running a monte carlo simulation to price an exotic (simple bs-dynamics). If I generate more than 1 timestep per year, will this effect my price because I am implicitly assuming that the continuous forward rate is constant over the timestep? I guess if it is introducing a lot of error I should linearly interpolate based on the step. Any thoughts? I have the same question about the volatility because I have atmf vols for each year (some are already linearly interpolated because of liquidity issues). -a

the question is: why are you "implicitly assuming that the continuous forward rate is constant over the timestep" if you "have a continuous forward rate for each year from 1 to 10 years"?

The significance of this effect depends entirely on what you are valuing. For a long-term bond option, interpolation shouldn't matter much unless the yield curve is very steep. For a quarterly interest rate swap, you have to interpolate to get a good answer. For some products, such as variance swaps, the kinks introduced by linear interpolation will kill you, you'll have to use a spline or some other smooth interpolation algorithm.

I am pricing a highly specialized lookback option so the vega is very high. I tried applying a cubic spline to the vols and rates but that actually reduced the price slightly. When I use stochastic vol, I get prices closer to the dealer's quotes, but I have reason to believe that they are not using a stochastic vol model. Any idea of what could be going on here?

Does the value depend more on the shape of the yield curve at a point in time, or the movement in a single tenor interest rate over time? For example, an option on the maximum spread between the 10 year and 2 year rate at any one time would depend on the shape, while an option on the maximum minus the minimum two-year rate over the period would depend on the movements over time. I realize the answer may be somewhere in between, but we have no good models for those kinds of options.Different types of models are used for the two extremes.

I would have to say that it depends more on the shape at a single point in time.

Then the problem is not likely to be with the interpolation scheme, unless you have a highly exotic option. It's more likely that your yield curve is not evolving naturally. Have you looked at some typical simulated future yield curves?

Yes, I am using a simple 1 factor Hull-white dynamics for the moment. I think the problem was with the volatility I was using. It seems that I was using lower volatility than was actually occuring (i forgot to bootstrap to get the forward vol). Now my price is coming in at mid-market like I would expect. Thanks for clearing up the issue about the interpolation, I realised that after bootstrapping correctly the interpolation scheme wasn't a big issue, especially on the rate side.-a