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.
- 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.
- I run a monte carlo simulation sampling from this distribution.
- 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
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.