CVA and vulnerable options pricing by correlation expansions

Abstract

We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in presence of the Wrong Way Risk (WWR) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in [2]. We compare the numerical performance of such a method with that recently proposed by Brigo et al. ([8], [10]) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.

On a convergent power series method to price defaultable bonds in a Vasicek-CIR model

“…Once the price functional representation is written, the main issue is the estimation of its derivatives, that we could obtain in our case. Employing estimates of completely different type, similar results were proven in [4] under constant interest rate for a forward contract, and in [2] and [3], for option pricing, so providing, the same as here, approximation formulas with much shorter computational times than Monte Carlo simulations.…”

“…The advantage of our parameter choice resides in the fact that expanding at zero correlation often allows exploiting semi-explicit expressions under independence of the driving processes. We finally remark that our methodology extends quite easily to include more factors in the model, as shown in [4].…”

Evaluation and Management of Intangible Assets of High-Tech Enterprises from the Perspective of Monte Carlo and Network Security

“…In the literature review on the study of the usefulness of accounting surplus in Barrulet's years, it is pointed out that the low level of determination coefficient reflects the reduced usefulness of accounting information. However, in contrast to the increasing investment in intangible assets, it can be known that the accounting system cannot truthfully reflect the intangible assets [12]. It is one of the decisive factors leading to the decline of value relevance.…”

Pricing vulnerable options in a hybrid credit risk model driven by Heston–Nandi GARCH processes

“…Vulnerable options refer to financial derivatives subject to default risk of the option's issuers, and they are widely traded in over-the-counter (OTC) markets. As of the first half of 2019, 3.9 trillion dollars (in terms of notional amounts) option contacts were traded in OTC markets 1 . The bespoke nature and the flexibility in terms of product design have helped OTC markets to thrive.…”

“…In this paper, we consider vulnerable options in a hybrid credit risk model. The model will 1 Resource: BIS, OTC derivatives statistics, https://www.bis.org/statistics/derstats.htm 2 A partial list of the studies on this topic includes Rich (1996), Klein and Inglis (1999), Klein incorporate the attractive features of both structural and reduced-form models. Hybrid credit risk models were initiated by Madan and Unal (2000), who investigate the pricing issue of risky debt in a hazard rate model with two factors being the values of the firm's assets and the interest rate.…”