Related papers: Derivatives Discounting Explained
The recent crisis and the following flight to simplicity put most derivative businesses around the world under considerable pressure. We argue that the traditional modeling techniques must be extended to include product design. We propose a…
The Cheap Gradient Principle (Griewank 2008) --- the computational cost of computing the gradient of a scalar-valued function is nearly the same (often within a factor of $5$) as that of simply computing the function itself --- is of…
Banks must manage their trading books, not just value them. Pricing includes valuation adjustments collectively known as XVA (at least credit, funding, capital and tax), so management must also include XVA. In trading book management we…
Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process {\xi} with memory as e.g. a L\'evy semi-stationary process.…
We introduce an approximation strategy for the discounted moments of a stochastic process that can, for a large class of problems, approximate the true moments. These moments appear in pricing formulas of financial products such as bonds…
We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic…
We introduce two quantum algorithms to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) of financial derivatives using quantum computers: the first by applying existing ideas from quantum risk analysis to derivative…
This paper presents a discrete--time equity derivatives pricing model with default risk in a no--arbitrage framework. Using the equity--credit reduced form approach where default intensity mainly depends on the firm's equity value, we…
This paper presents a convenient framework for modeling default process and pricing derivative securities involving credit risk. The framework provides an integrated view of credit valuation adjustment by linking distance-to-default,…
The role of collateral in derivative pricing has evolved beyond credit risk mitigation, particularly following the global financial crisis, when funding costs and basis spreads became central to valuation practices. This development…
We consider the problem of computing the Value Adjustment of European contingent claims when default of either party is considered, possibly including also funding and collateralization requirements. As shown in Brigo et al. (\cite{BLPS},…
Value adjustment of uncollateralized trades is determined within a risk-neutral pricing framework. When hedging such trades, investors cannot freely trade protection on their own name, thus facing an incomplete market. This fact is…
In this article, we analyze two modeling approaches for the pricing of derivative contracts on a commodity index. The first one is a microscopic approach, where the components of the index are modeled individually, and the index price is…
Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump-diffusions to jointly price the term structures of dividends and…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized…
During the COVID-19 pandemic, many institutions have announced that their counterparties are struggling to fulfill contracts.Therefore, it is necessary to consider the counterparty default risk when pricing options. After the 2008 financial…
This paper provides intuition on the relationship of accrual and mark-to-market valuation for cash and forward interest rate trades. Discounted cashflow valuation is compared to spread-based valuation for forward trades, which explains the…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
Dividend discount models have been developed in a deterministic setting. Some authors (Hurley and Johnson, 1994 and 1998; Yao, 1997) have introduced randomness in terms of stochastic growth rates, delivering closed-form expressions for the…