# Treasury futures wild card option (Monte carlo simulation)

I recently joined a bulge bracket bank in New York City trading the long-end but mostly doing a lot of analysis until I get up to speed. I'm working on the Wildcard model which is going to be an important theme heading into the futures roll cycle and the senior trader asked me to look into a Monte Carlo Simulation. I've been searching around in the literature but have not been able to find something that I can put together. He doesn't want anything quanty, just a quick Monte Carlo model.

Let me know if this is the right thought process.

1. I have a distribution of 3pm - 6pm moves during the delivery period in the CTD. I have collected this data over the past two years. I guess I can also just assume a normal distribution for simplicity.
2. I run a monte carlo simulation sampling from this distribution.
3. For each day during the delivery period, I extract a value and determine whether it is optimal to exercise or wait. I believe this depends on a breakeven formula where the move in the bond price is greater than Gross Basis * CF /(1-CF). If the move in the CTD is sufficient, I exercise the wildcard option and sell the tail of my position for a profit.

Let's assume the delivery period is 15 days so I have the following:

Simulation 1: 5th day wildcard exercise. Profit is $0.25 Simulation 2: 1st day wildcard exercise. Profit is$0.15

Simulation 3: 15th day wildcard exercise. Profit is $0.05 Simulation 4: No wild card exercise Simulation 5: No wild card exercise Simulation 6: 8th day wildcard exercise. Profit is$0.01

....

....

Simulation 10000

Now, I am confused how I figure out the wildcard value from here. Do I take the average of all these profits to determine the expected profit and that is my wildcard value? In this case, it'll be average of the above divided by 10000. Do I have to subtract the carry for the 15 days in the delivery period?

So essentially, Wildcard = E[Payoff from Wildcard exercise] - Carry

Any help is appreciated. This is just a simple model to start with. I remember doing something like this for Black Scholes options in school where I simulate the stock prices across thousands of paths. At the terminal path, I extract the payoff and discount all the payoffs back to the present value. I imagine what I am doing now is similar to an American options because it can be exercised early.

I’d say you have the right ideas, and I’ll make a few comments:

A) yields have been very volatile for the last couple months, and might be expected to be volatile for the next few cycles also. Therefore using historical data for the last 2yrs might underestimate future volatility. Maybe weight it towards recent data more.

B) theoretically an American option wouldn’t be exercised early in the cycle unless it is ‘deep’ in the money, whereas I think you’ve assumed immediate exercise if in the money even by a little bit. This means you’re underestimating it slightly. But fair enough you are looking for something simple.
C) your formula looks correct to me, but I don’t see the need to subtract ‘carry’. ‘Carry’ is already contained in gross basis.
D) what are you assuming about Gross Basis? It should amortize from its starting value to zero on the last day.

Good luck

• Thanks this is helpful information A) I guess I can use a normal distribution and maybe increase the vol assumption B) Isn't it the case that if the move in the tail of the position of the bond exceeds the carry that you forgo, then it is optimal to sell off this tail and exercise delivery. C) Thanks, so carry is not necessary D) I calculate Gross Basis on the first day that I can exercise the wild card. The formula would be Gross Basis = Spot Price - CF* Futures. Each day, I reduce the Gross Basis by the carry in the bond. Isn't Gross Basis = Net Basis + Carry right? May 14 at 21:41
• A)agreed B) well let’s say it is day 1 and the move only slightly exceeds the break even, then you might say that you will wait for day 2 to see if you get a bigger move. D) agreed
– dm63
May 15 at 4:43