Related papers: Derivatives Discounting Explained
In this paper we propose a new model for pricing stock and dividend derivatives. We jointly specify dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate non-negative. In its simplest…
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where…
This paper develops an XVA (costs) analysis of centrally cleared trading, parallel to the one that has been developed in the last years for bilateral transactions. We introduce a dynamic framework that incorporates the sequence of…
We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not…
We extend the scope of differential machine learning and introduce a new breed of supervised principal component analysis to reduce dimensionality of Derivatives problems. Applications include the specification and calibration of pricing…
In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) L\'evy processes to model the underlying asset of contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy…
The smooth function reconstruction needs to use derivatives. In 2010, we used the gradually varied derivatives to successfully constructed smooth surfaces for real data. We also briefly explained why the gradually varied derivatives are…
We apply the concepts of utility based pricing and hedging of derivatives in stochastic volatility markets and introduce a new class of "reciprocal affine" models for which the indifference price and optimal hedge portfolio for pure…
An uncollateralized swap hedged back-to-back by a CCP swap is used to introduce FVA. The open IR01 of FVA, however, is a sure sign of risk not being fully hedged, a theoretical no-arbitrage pricing concern, and a bait to lure market risk…
People often face trade-offs between costs and benefits occurring at various points in time. The predominant discounting approach is to use the exponential form. Central to this approach is the discount rate, a unique parameter that…
Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging…
We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion…
In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at…
Crises challenge client XVA management when continuous collateralization is not possible because a derivative locks in the client credit level and the provider's funding level, on the trade date, for the life of the trade. We price XVA…
We present a high-level framework that explains why, in practice, different pricing models calibrated to the same vanilla surface tend to produce similar valuations for exotic derivatives. Our approach acts as an overlay on the Monte Carlo…
Although not a formal pricing consideration, gap risk or hedging errors are the norm of derivatives businesses. Starting with the gap risk during a margin period of risk of a repurchase agreement (repo), this article extends the…
We consider the problem of designing a derivatives exchange aiming at addressing clients needs in terms of listed options and providing suitable liquidity. We proceed into two steps. First we use a quantization method to select the options…
We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…
In this paper, we propose a neural network-based method for CVA computations of a portfolio of derivatives. In particular, we focus on portfolios consisting of a combination of derivatives, with and without true optionality, \textit{e.g.,}…
We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox-Ross-Rubinstein (CRR) pricing model. The main tool used in the paper for cleaning up the reasoning is applying static…