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Pricing and hedging vulnerable option with funding costs and collateral

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  • Han, Xingyu

Abstract

We explore the valuation and hedging strategies of a European vulnerable option with funding costs and collateralization for local volatility models. It is found that, in the absence of arbitrage opportunities, the option price must lie within a no-arbitrage band. The boundaries of no-arbitrage band are computed as solutions to backward stochastic differential equations (BSDEs in short) of replicating strategy and offsetting strategy. Under some conditions, we obtain the closed-form representations of the no-arbitrage band for local volatility models. In particular, the fully explicit expressions of the no-arbitrage band for Black–Scholes model and the constant elasticity of variance (CEV) model with time-dependent parameters are derived. Furthermore, we provide a strategy for the option holder by using the risky bond issued by the option writer to hedge the remaining potential losses. By virtue of numerical simulation, the impact of the default risk, funding costs and collateral can be observed visually.

Suggested Citation

  • Han, Xingyu, 2018. "Pricing and hedging vulnerable option with funding costs and collateral," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 103-115.
    • Handle: RePEc:eee:chsofr:v:112:y:2018:i:c:p:103-115
    DOI: 10.1016/j.chaos.2018.04.042
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    1. Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.

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    More about this item

    Keywords

    European vulnerable option; Funding spreads; Collateral; Local volatility; Backward stochastic differential equations;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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