Innovations in Derivatives Markets: Fixed Income Modeling, by Kathrin Glau, Zorana Grbac, Matthias Scherer, Rudi Zagst

By Kathrin Glau, Zorana Grbac, Matthias Scherer, Rudi Zagst

This ebook provides 20 peer-reviewed chapters on present elements of derivatives markets and by-product pricing. The contributions, written through best researchers within the box in addition to skilled authors from the monetary undefined, current the state-of-the-art in:

• Modeling counterparty credits danger: credits valuation adjustment, debit valuation adjustment, investment valuation adjustment, and other way risk.

• Pricing and hedging in fixed-income markets and multi-curve interest-rate modeling.

• fresh advancements referring to contingent convertible bonds, the measuring of foundation spreads, and the modeling of implied correlations.

The fresh monetary problem has forged great doubts at the classical view on by-product pricing. Now, counterparty credits possibility and liquidity matters are fundamental elements of a prudent valuation method and the reference rates of interest are represented through a mess of curves in keeping with their assorted classes and maturities.

A panel dialogue integrated within the booklet (featuring Damiano Brigo, Christian Fries, John Hull, and Daniel Sommer) at the foundations of modeling and pricing within the presence of counterparty credits chance presents fascinating insights at the debate.

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Extra info for Innovations in Derivatives Markets: Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation

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Net of credit) of the funding valuation adjustment. We now take a number of heuristic steps. A more formal analysis in terms of FBSDEs or PDEs is, for example, provided in Brigo et al. [15]. For simplicity, we first switch to the default-free market filtration (Ft )t≥0 . This step implicitly assumes a separable structure of our complete filtration (Gt )t≥0 . We are also assuming that the basic portfolio cash flows π(0, t) are Ft -measurable and that default times of all parties are conditionally independent, given filtration F .

Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs. 00686. A refined version of this paper appears in the present volume (2015) Nonlinearity Valuation Adjustment 35 16. : Partial differential equation representations of derivatives with counterparty risk and funding costs. J. Credit Risk 7(3), 1–19. com/abstract=1605307 (2011) 17. : In the balance. Risk Mag. (2011) 18. : Valuation of the early-exercise price for options using simulations and nonparametric regression.

This added recursion requires that we solve the funding and hedging strategies simultaneously. For example, if the dealer applies a delta-hedging strategy we can write, heuristically, Ht j = ∂ V¯ ∂X tj Xtj ≈ V¯t j+1 − (1 + Δt j f˜t j )V¯t j Xtj , X t j+1 − (1 + Δt j f˜t j )X t j (23) and we obtain, in the case of rehypothecation, the following system of nonlinear equations Nonlinearity Valuation Adjustment ⎧ ⎪ ⎪ Ft j − ⎪ ⎪ ⎨ 23 f˜ Pt j (t j+1 ) Pt j (t j+1 ) V¯t Et j Ξt j (V¯t j+1 ) = 0, −(1+Δt j f˜t )V¯t Ht j − X j+1 −(1+Δt f˜ j )X j X t j = 0, ⎪ ⎪ t j+1 j tj tj ⎪ ⎪ ⎩¯ Vt j = Ft j + Ct j + Ht j , (24) where all matrix operations are on an element-by-element basis.

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