Derivative Pricing under Funding Costs and Bilateral Counterparty Risk: A Burgard-Kjaer and XVA Comparison
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- This thesis studies the impact of funding costs and bilateral counterparty risk on deriva- tive valuation within the Burgard–Kjaer framework. While classical Black–Scholes pricing assumes frictionless and default-free markets, modern OTC derivative markets are signif- icantly affected by credit and funding considerations. The analysis compares unilateral derivatives, represented by a European call option, with bilateral derivatives such as an equity forward and an interest rate forward. The Burgard–Kjaer pricing equations are implemented numerically using Crank–Nicolson fi- nite differences and Monte Carlo simulations, and the results are compared with a sim- plified modern XVA framework combining CVA, DVA and FVA adjustments. The results show that the Burgard–Kjaer and additive XVA approaches produce al- most identical adjustments for unilateral derivatives. However, for bilateral derivatives, the Burgard–Kjaer adjustments become significantly larger, reaching differences close to a factor of three compared with the simplified XVA framework. These results suggest that additive XVA decompositions may remain acceptable for strongly unilateral products, but can materially underestimate valuation adjustments once bilateral exposure becomes significant.