Pricing Credit Default Swaps when Interest Rate Process and Hazard Rate Process are Stochastic

2007 ◽  
Author(s):  
Fangxia Lin
Keyword(s):  
Interest Rate ◽  
Hazard Rate ◽  
Credit Default Swaps ◽  
Rate Process ◽  
Credit Default

PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK

2013 ◽  
Vol 16 (02) ◽  
pp. 1350007 ◽  
Author(s):  
DAMIANO BRIGO ◽  
AGOSTINO CAPPONI ◽  
ANDREA PALLAVICINI ◽  
VASILEIOS PAPATHEODOROU
Keyword(s):  
Interest Rate ◽  
Credit Derivatives ◽  
Credit Default Swaps ◽  
Credit Spread ◽  
Counterparty Risk ◽  
Default Correlation ◽  
Dynamical Models ◽  
Credit Default ◽  
The Impact

This article is concerned with the arbitrage-free valuation of bilateral counterparty risk through stochastic dynamical models when collateral is included, with possible rehypothecation. The payout of claims is modified to account for collateral margining in agreement with International Swap and Derivatives Association (ISDA) documentation. The analysis is specialized to interest-rate and credit derivatives. In particular, credit default swaps are considered to show that a perfect collateralization cannot be achieved under default correlation. Interest rate and credit spread volatilities are fully accounted for, as is the impact of re-hypothecation, collateral margining frequency, and dependencies.

Types of Swaps

2019 ◽  
pp. 199-230
Author(s):  
Alan N. Rechtschaffen
Keyword(s):  
Interest Rate ◽  
Regulatory Reform ◽  
Credit Default Swaps ◽  
Cash Flows ◽  
Over The Counter ◽  
Credit Default ◽  
Interest Rate Swaps ◽  
Payment Schedule ◽  
Reference Amount

A swap is a bilateral over-the-counter derivatives contract in which two parties agree to exchange cash flows on a “notional amount” over a period of time. The notional amount is a reference amount upon which the payment formula is based. The parties exchange cash flows pursuant to an agreed-upon payment schedule, made up of one or more payment dates throughout the life of the contract. Cash flows are computed by applying the agreed-upon formula relating to each party's respective set of payments of the swap to a notional amount, that is, a hypothetical underlying value that does not necessarily itself change hands. This chapter discusses “plain vanilla” interest rate swaps, currency swaps, credit-default swaps, and the move toward regulatory reform.

NEW MODEL FOR PRICING QUANTO CREDIT DEFAULT SWAPS

2019 ◽  
Vol 22 (03) ◽  
pp. 1950003
Author(s):  
A. ITKIN ◽  
V. SHCHERBAKOV ◽  
A. VEYGMAN
Keyword(s):  
Exchange Rate ◽  
Interest Rate ◽  
Foreign Exchange ◽  
Credit Derivatives ◽  
Partition Of Unity ◽  
Credit Default Swaps ◽  
Foreign Exchange Rate ◽  
New Model ◽  
Credit Default ◽  
Risky Bonds

We propose a new model for pricing quanto credit default swaps (CDS) and risky bonds. The model operates with four stochastic factors, namely: the hazard rate, the foreign exchange rate, the domestic interest rate, and the foreign interest rate, and allows for jumps-at-default in both the foreign exchange rate and the foreign interest rate. Corresponding systems of partial differential equations are derived similar to how this is done by Bielecki et al. [PDE approach to valuation and hedging of credit derivatives, Quantitative Finance 5 (3), 257–270]. A localized version of the Radial Basis Function partition of unity method is used to solve these four-dimensional equations. The results of our numerical experiments qualitatively explain the discrepancies observed in the marked values of CDS spreads traded in domestic and foreign economies.

scholarly journals Asymptotic Analysis for One-Name Credit Derivatives

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yong-Ki Ma ◽  
Beom Jin Kim
Keyword(s):  
Asymptotic Analysis ◽  
Stochastic Volatility ◽  
Credit Derivatives ◽  
Approximate Solutions ◽  
Credit Default Swaps ◽  
Rate Process ◽  
Yield Curves ◽  
Defaultable Bond ◽  
Credit Default ◽  
Bond Options

We propose approximate solutions to price defaultable zero-coupon bonds as well as the corresponding credit default swaps and bond options. We consider the intensity-based approach of a two-correlated-factor Hull-White model with stochastic volatility of interest rate process. Perturbations from the stochastic volatility are computed by using an asymptotic analysis. We also study the sensitive properties of the defaultable bond prices and the yield curves.

scholarly journals CVA AND FVA TO DERIVATIVES TRADES COLLATERALIZED BY CASH

2015 ◽  
Vol 18 (05) ◽  
pp. 1550035 ◽  
Author(s):  
LIXIN WU
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rate ◽  
Credit Default Swaps ◽  
Call Option ◽  
Interest Rate Swap ◽  
Pricing Process ◽  
Credit Default ◽  
Credit Valuation Adjustment ◽  
Rate Swap

In this paper, we consider replication pricing of derivatives that are partially collateralized by cash. We let issuer replicate the derivatives payout using shares and cash, and let buyer replicate the loss given the counterparty default using credit default swaps. The costs of funding for replication and collateral posting are taken into account in the pricing process. A partial differential equation (PDE) for the derivatives price is established, and its solution is provided in a Feynman–Kac formula, which decomposes the derivatives value into the risk-free value of the derivative plus credit valuation adjustment (CVA) and funding valuation adjustment (FVA). For most derivatives, we show that CVAs can be evaluated analytically or semi-analytically, while FVAs as well as the derivatives values can be solved recursively through numerical procedures due to their interdependence. In numerical demonstrations, continuous and discrete margin revisions are considered, respectively, for an equity call option and a vanilla interest-rate swap.

xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT

2020 ◽  
Vol 23 (01) ◽  
pp. 2050006
Author(s):  
LIXIN WU ◽  
DAWEI ZHANG
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Liquidity Risk ◽  
Credit Default Swaps ◽  
Interest Rate Swap ◽  
Funding Liquidity ◽  
Credit Default ◽  
Risk Neutral ◽  
Default Risks ◽  
Rate Swap

xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

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