| The research characterizes the arbitrage-free dynamics of forward LIBOR rates and forward swap rates, in the presence of stochastic volatility and jumps. The jumps are modeled through marked point processes, which allow randomness of jump sizes and dependence between jumps and stochastic volatility. Jumps term captures the effect of the release of macroeconomic events and interventions of Federal Reserve. The stochastic volatility is new and highly correlated with the forward rate itself. By formulating a tractable subclass of models, I provide pricing formulas for some most heavily traded derivatives in the interest rate derivatives market: interest rate caps and swaptions. |
