Derivation of the ‘rearranged’ formula for the Crank-Nicolson scheme. Implementation in C++ of the pricing of an American put option, using the Crank-Nicolson scheme. Comments on the way to deal with the practical choices facing a finite difference implementer (e.g. the boundary conditions)....

We investigate the most common type of blockchain-based decen- tralized exchange, which are known as constant function market makers (CFMMs). We examine the the market microstructure around CFMMs and present a model for valuing the liquidity provider (LP) mechanism and estimating the value of...

This article discusses the problem of pricing discretely sampled variance swaps under the Heston stochastic volatility model with stochastic interest rate and stochastic dividend yield. In particular, our modelling framework consists of a stochastic interest rate driven by Hull-White (HW) or...

The small-maturity implied volatility of an asset pricing model is fully determined by the asymptotics of traded option prices, and thus model-free expressions are available. We show how by sharpening one such expression it is possible to derive a general formula for the leading order of the...

Many attempts have been made to estimate market characteristics from options prices, none more well known than the Black Scholes model. Yet, no options pricing model is without significant criticism. And none are consistent with the characteristics of the market discussed in this paper. Prior to...

Considering the fair strike values of variance and volatility swaps, we use a stochastic volatility model in which the log volatility is given by a fractional Ornstein-Uhlenbeck process with two versions; a stationary version and a version with a deterministic initial value. Under these...

In this article, we test performance persistence and measure the historical, the implied volatility, the credit spread volatility and the value at risk,VaR, of the credit derivatives swaptions contracts. We examine contracts of US leveraged loans, mortgage backed securities, high grade corporate...

Real options are a type of investment choice that supports decision-makers in making better strategic management decisions while simultaneously reducing uncertainty in investments. In this paper, we present a new model to help investors handle uncertain investment environments flexibly. First,...

We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest rates. For each model, we include detailed derivations...

Derivatives pricing changed drastically in 2007-2008, following the financial crisis. The failureof the Lehman Brothers refuted the myth that ”AAA” rated financial institutions cannotdefault. Basel III was introduced and implemented to reinforce existing financial market regulationsand...