(Monte Carlo) correlation of daily vs qtly time series?

CFA General
#1

I want to generate Monte Carlo paths for the price of oil and a company’s Net Income. 1. What oil price should I use to correlate with each quarter’s NI figure? The average daily price? The price on the last day of the quarter? 2. How do I generate the paths to project the next 8 quarters of oil price and NI?

#2

I’ll bet you don’t. Unless there’s something very path dependent about NI on oil (and I can’t imagine what that might be), as soon as you specify a model for oil prices and a relationship with NI, you have a stochastic integral and you should evaluate that, not try to simulate the answer. Of course, like anything else the oil price process is full of distribution changes, outside influences, weird jumps, possibly mean reverting forces, and so on. Modelling oil prices is an endless project and it’s hard to believe you get much out of the project when you get done.

#3

I’m projecting a firm over time with a real option that’s dependent on oil price. I think it has to be path dependent. As you say, lots of religion in generating oil prices; I’m using Schwartz&Smith’s 2000 approach (mean reversion, no jumps), in part because it gives analytic values for vanilla option prices as I move forward in time. Regardless of whether this is the best process, I still have this lingering question about generating values when I’ve calibrated to daily (oil) and quarterly (NI) historicals.

#4

What does ole’ Schwartz & Smith say about the future price of oil?

#5

DarienHacker, there are two approaches you can use. The first one, choose a model that you like, calibrate it (fit parameters) and then run Monte-Carlo simulations using the model. The second approach would be using historical returns. For example, you can take 10 year daily returns of oil (for example, +1%, -.5%, etc). Then use rolling windows of 8 quarter returns (for example, Jan 1, 2000-Dec 31, 2001;Jan 2, 2000-Jan 1, 2002, …, Jan 1, 2005 - Dec 31, 2006) if you have data from Jan 1, 2002 - Dec 31, 2006. I hope that helps.

#6

virginCFAhooker Wrote: ------------------------------------------------------- > What does ole’ Schwartz & Smith say about the > future price of oil? Looks a lot like (today’s price)e^rt

#7

Thanks maratikus.