How to simulate selling straddles?

Here's what I'm trying to do:
1. Fill an array with artificial prices which daily changes are normally distributed.
2. Simulate one year of selling 7 days straddles. Sell ATM call and put, take prices from BS formula. For implied volatility use future volatility (calculated on 7 days ahead). Calculations are done with non-centered volatility, result is multiplied by (0.95 + rand(15)/100.0). This is to simulate that IV is usually higher than HV.

I always thought, that if I sell vol which is higher than future realized, then I will be profitable. It seems I have to multiply realized vol by about 1.3 and use this number as IV to make selling straddles profitable. Is this expected? (no commissions in calculations).

 

Your simulations will differ from reality because of this assumption. This assumption is incorrect in reality so your simulation will actually end up preparing for real life through testing a faulty model.

A better approach is bactesting on actual historical data and then if you want to simulate, produce data which mirrors the non-normal characteristics of historical data.

 

This assumption should make things even more in my favour, so it doesn't answer my question.

 

You have already mentioned that IV is usually higher than HV.
1)My first question would be which product are you simulating straddles on? 2) On this product, what is the difference between actual HVs and IVs? Is it 1.3:1 or more in real life. I have never run this test, so I am just trying to put forward my thoughts.

It is an interesting question - if I get time, I will do my own study on this.

 

fair point.

 

I sell straddles every month and as Kenny Rogers said:

"Every straddle's a winner, and every straddle's a loser."

So much is dependent on how/when you adjust.

If you run the data from open until expiration with no adjustments, that's fine, but it may not give you a realistic picture.

 

The straddle PL should be dependent on the difference between implied and realised vol. But since there is no delta hedging and each straddle will be on a single strike only, the straddle PL would have a huge variance.

If you have a copy of the Wilmott book, he gives somewhere equations for both the expected straddle PL and the variance of the PL

 

He is already simulating, so a large variance or small, he should be getting the correct mean value. His question is: when he is using IVs > HVs, then also straddle PL is negative. Why?

 

Yes, it's expected. You're not delta-hedging the straddle, innit?

 

As noted by Martinghoul and others, this is incorrect.

Consider a market which exhibits a steady climb over a period of time.

Since returns are almost constant, realized and implied volatility (the standard deviation of returns) will be almost zero.

So selling calls will lose a huge amount of money.

To make money selling options, BOTH of the following must be true:

(1) realized volatility must be lower than implied volatility

(2) the market must not trend

To get around (2), you would have to delta hedge constantly (or at least periodically).