We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local...

Risk-free rates (RFRs) play a central role in the reform of interest rate benchmarks. We study a model for RFRs driven by a general affine process. In this context, under minimal assumptions, we derive explicit valuation formulas for forward-looking and backward-looking caplets/floorlets,...

Interest rate instruments are typically priced by creating a non-arbitrage replicating portfolio in a risk-neutral framework. Bespoke instruments with timing, quanto and other adjustments often present arbitrage opportunities, particularly in complete markets where the difference can be...

Interest rate swaps are an actively traded product in the financial marketplace and are popular for hedging mortgage and corporate loan exposures against rises in interest rates. Asset swaps on the other hand provide a form of asset financing, where investors borrow funds to purchase an asset,...

In this paper we outline the Lagrangian constrained optimization method to solve complex problems subject to constraints. Firstly we summarize the Lagrangian constrained optimization routine. Secondly we outline a detailed implementation strategy. Thirdly and finally we provide example and solve...