On cash settled IRR-swaptions and Markov functional modeling

In this paper, we show how to consistently price cash settled Internal Rate of Return (IRR)-swaptions and derivatives on these contracts. There are several results worth highlighting. First, if we know at what fixed coupon an IRR-swap values to par, we can compute the price of any IRR-swaption in a way consistent with absence of arbitrage. We show that this fixed coupon, denoted the IRR-forward, carries an additional convexity adjustment. The size of the adjustment depends mainly on the shape of the volatility surface but also on the skew of the forward. The largest convexity adjustments are seen for IRR-forwards referencing long tenors and long expiries. Second, we show that any Markov functional technique, relating a given term-structure model to the market observed IRR-swaptions, should be carried out with respect to the corresponding forward measure. The modification of the forward swap rate is further shown to consistently value the fixed and the floating leg of the underlying IRR-swap correctly.