Pricing(Cost)

n Vanilla Finance's Profit Swap Contract, we use the classic Longstaff-Schwartz Method to price the contract. In the product, the Price of Contract is also referred to as Cost.

Introduction to the Longstaff-Schwartz Method

The Longstaff-Schwartz Method is a well-known approach for pricing American-style options. These types of options can be exercised at any time before thy expire, making their valuation more complex than European options, which can only be exercised at maturity. The Longstaff-Schwartz Method offers a solution by using a combination of Monte Carlo simulations and least squares regression to help determine when it’s optimal to exercise an option for maximum gain.

How It Works

1. Simulating Possible Futures:

   • The method first generates various possible future price paths for the underlying asset (e.g., a stock) using Monte Carlo simulations. These price paths represent different market scenarios over the life of the option.

2. Analyzing Each Scenario:

   • For each price path, it evaluates whether it’s better to exercise the option immediately (i.e., sell it) or hold it and wait for future gains. This is done by comparing the immediate payoff (the amount you’d get if you exercised the option) with the continuation value (the estimated future profit from holding the option).

3. Regression to Estimate Future Value:

   • The least squares regression is applied to predict the continuation value. This uses past data to estimate the potential future payoff based on how the asset’s price has moved. For example, if the stock price is expected to rise, the continuation value would be higher, and it might be worth holding the option longer.

4. Making the Best Decision:

   • At each point in time, the method helps decide whether to exercise the option or hold it, ensuring that the decision maximizes potential profits.

5. Final Valuation:

   • After simulating multiple price paths and making exercise decisions for each, the method averages the payoffs and discounts them back to present value, giving the final valuation of the option.

Formulas Used:

1. Monte Carlo Simulation

1. 

3.Optimal Exercise Decision:

4.Discounting Payoff: