237 research outputs found
CVA and vulnerable options pricing by correlation expansions
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 \cite{AS}. We compare the
numerical performance of such a method with that recently proposed by Brigo et
al. (\cite{BR18}, \cite{BRH18}) 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.Comment: 21 page
Funding, repo and credit inclusive valuation as modified option pricing
We take the holistic approach of computing an OTC claim value that
incorporates credit and funding liquidity risks and their interplays, instead
of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting
nonlinear mathematical problem features semilinear PDEs and FBSDEs. We show
that for the benchmark vulnerable claim there is an analytical solution, and we
express it in terms of the Black-Scholes formula with dividends. This allows
for a detailed valuation analysis, stress testing and risk analysis via
sensitivities.Comment: 1 figur
Transition probability of Brownian motion in the octant and its application to default modeling
We derive a semi-analytic formula for the transition probability of
three-dimensional Brownian motion in the positive octant with absorption at the
boundaries. Separation of variables in spherical coordinates leads to an
eigenvalue problem for the resulting boundary value problem in the two angular
components. The main theoretical result is a solution to the original problem
expressed as an expansion into special functions and an eigenvalue which has to
be chosen to allow a matching of the boundary condition. We discuss and test
several computational methods to solve a finite-dimensional approximation to
this nonlinear eigenvalue problem. Finally, we apply our results to the
computation of default probabilities and credit valuation adjustments in a
structural credit model with mutual liabilities
CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?
We present a dialogue on Funding Costs and Counterparty Credit Risk modeling,
inclusive of collateral, wrong way risk, gap risk and possible Central Clearing
implementation through CCPs. This framework is important following the fact
that derivatives valuation and risk analysis has moved from exotic derivatives
managed on simple single asset classes to simple derivatives embedding the new
or previously neglected types of complex and interconnected nonlinear risks we
address here. This dialogue is the continuation of the "Counterparty Risk,
Collateral and Funding FAQ" by Brigo (2011). In this dialogue we focus more on
funding costs for the hedging strategy of a portfolio of trades, on the
non-linearities emerging from assuming borrowing and lending rates to be
different, on the resulting aggregation-dependent valuation process and its
operational challenges, on the implications of the onset of central clearing,
on the macro and micro effects on valuation and risk of the onset of CCPs, on
initial and variation margins impact on valuation, and on multiple discount
curves. Through questions and answers (Q&A) between a senior expert and a
junior colleague, and by referring to the growing body of literature on the
subject, we present a unified view of valuation (and risk) that takes all such
aspects into account
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