A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub-additive axiom to preserve the original difference between the numeraire of...

We investigate the effect of including variance derivatives as calibration and hedging instruments for pricing and hedging exotic structures. This is studied empirically using market data for SPX and VIX derivatives applied in a stochastic volatility jump diffusion model

Even if the name futures indicates a simple instrument, bond futures are complex. Several special features are embedded in the instrument. In particular the future is not written on one specific bond but on a basket of bonds, from which the short side can deliver the cheapest. This paper focuses...

We discuss the valuation of credit derivatives in extreme regimes such as when the time-to-maturity is short, or when payoff is contingent upon a large number of defaults, as with senior tranches of collateralized debt obligations. In these cases, risk aversion may play an important role,...

Implied volatility and other forward-looking measures of option-implied uncertainty help investors carefully evaluate market sentiment and expectations. We construct several measures of implied uncertainty in European government bond futures. In the first part, we create new volatility indices,...

We compile option-implied tail loss and gain measures based on a deep out-of-the- money option pricing formula derived by applying ‘extreme value theory', and then use these measures to investigate the information content of option-implied tail risk on the future returns of the underlying...

In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the contract's maturity the contract is perfectly hedged. We...