Speaker
Description
We propose and compare two approaches for efficient calculation of an exposure profile for interest rate derivatives linked to Russian OIS rate (RUB_RUONIA_OIS) for the purpose of computing two credit risk metrics: CVA (Credit Value Adjustment) and PFE (Potential Future Exposure).
In the industry, the standard approach for pricing complex derivatives is the Monte Carlo method, in which a certain stochastic differential equation (SDE) for the interest rate process is postulated, a set of paths is generated accordingly, and on each path the sum of discounted cash flows from the derivative is computed, after which these sums are averaged to obtain the price at the initial time. To compute CVA and PFE metrics, it is necessary to compute not only the expectation of discounted future cash flows at the initial time, but also the so-called Continuation Values (CV), namely, the conditional expectations of discounted future cash flows, at each time step of each path.
We propose two approaches for computing Continuation Value at each time point ti. The first approach is called Regression-Based Monte Carlo and is based on the idea of approximating the Continuation Value function by a polynomial of the rate process. This approach is universal and works for any derivatives and any SDE generating the interest rate process. However, its accuracy and computational cost depend on the choice of basis functions, the polynomial degree, and the type of the derivative itself.
The second approach is analytical. Within the one-factor linear Gaussian model, for two main classes of products (interest rate swaps and caps), exact formulas for CV are derived, allowing one to compute the exposure for each path without additional approximation error and with minimal computational cost. The main disadvantages of the analytical approach include the fact that it does not work for derivatives with path-dependent payoffs, as well as the necessity to derive new analytical formulas in the event of changing the SDE governing the interest rate evolution.
For interest rate swaps with maturities of 1, 3, 5, and 10 years, we compute CVA using both approaches.
