I am assessing Monte Carlo framework for various derivatives. Current implementation of HullWhiteMonteCarloMethod as well as G2ppMonteCarloMethod are designed on schedules, where decision points are set on dates, where all floating rate coupons are starting at least at the decision point or later. That allows e.g. in case of IRS for using CashFlowEquivalent approach according to formula on page 20 in Marc’s book.
I am wandering, how would you approach implementation of Monte Carlo framework for measuring prices of derivative portfolios where observation dates are not coinciding with cash flow dates in underlying portfolios, e.g. decision points are set on equidistant grid, e.g. monthly intervals, and then valuation of IRS with quarterly payments on floating leg and annual fixed. Let’s say we are in a decision point, where the floating coupon has been fixed 2.5 months before that.
As I understand CashFlowEquivalent approach, assuming constant basis spread, it could be used for:
- the fixed leg,
- part of the floating leg, which would be trimmed to cash flows with interest periods starting after the decision points
- value of the floating coupon that has been fixed 2.5 months before the decision point.
The question is if you would then draw some number with brownian bridge, to determine what was the fixing of that Ibor rate, or used some interpolation scheme on the path?
Alternatively, would it be suitable to have floating leg CashFlowEquivalent trimmed in a way, that it is Beta from the fixing date accrued with some stochastic discount factor (which?) from the fixing date to the decision date less the discount factor from the coupon payment date?
The more sophisticated situation would be if we would decide to move to stochastic spreads. As I understand, in that case cash flow equivalent wouldn’t be suitable. Would you agree, that it would be better to have a visitor calculator, that would utilize state variables, and path integrals with volatility coefficients determining prices of instrument at any time depending on state variables rather then working on three dimensional matrix of discount factors?
I understand current design is concentrating on efficiency for pricing and market risk measurement of typical products, the necessity to think about problems as described above is appearing in case you want to produce PFE or expected exposure. If you would be so kind to share your thoughts on that, I will highly appreciate that.