Numeraire invariance is a well-known technique in option pricing and hedging theory. It takes a convenient asset as the numeraire, as if it were the medium of exchange, and expresses all other asset and option prices in units of this numeraire. Since the price of the numeraire relative to itself is identically 1 at all times, this reduces pricing and hedging to a market with zero-interest rates...

The previous studies have shown that the application of option contracts affects coordination supply chain. Though, based on authors’ research there appears to be no survey conducted measure effect hedging chain from quantitative viewpoint. Generally, it is assumed product price held fixed in hedging; however, competitors or partners might sell cheaper. This condition restricts hedger's opportu...

We propose the use of a classical tool in PDE theory, the parametrix method, to build approximate solutions to generic parabolic models for pricing and hedging contingent claims. We obtain an expansion for the price of an option using as starting point the classical Black&Scholes formula. The approximation can be truncated to any number of terms and easily computable error measures are available.

We present an explicit formula for European options on coupon bearing bonds and swaptions in the Heath-Jarrow-Morton (HJM) one factor model with non-stochastic volatility. The formula extends the Jamshidian formula for zero-coupon bonds. We provide also an explicit way to compute the hedging ratio (∆) to hedge the option with its underlying.

I explicitly work out closed form solutions for the optimal hedging strategies (in the sense of Bouchaud and Sornette) in the case of European call options, where the underlying is modeled by (unbiased) iid additive returns with Student-t distributions. The results may serve as illustrative examples for option pricing in the presence of fat tails.

We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of the graph of the option price, related to our strategy, demonstrates the ”skewness” inherent to the observational data.

proportional transaction costs using the utility-maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor’s basic portfolio selection problem without insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the bou...

This article illustrates the impact of both spot and option liquidity levels on option prices. Using implied volatility to measure the option price structure, our empirical results reveal that even after controlling for the systematic risk of Duan and Wei (2009), a clear link remains between option prices and liquidity; with a reduction (increase) in spot (option) liquidity, there is a correspo...

For asset prices that follow stochastic-volatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices, and to relate this behavior to the parameters of the stochastic volatility process. We also give applications, including risk-premium-based explanations of the biases in some näıve pricing and hedg...

Volatility derivatives are becoming increasingly popular as means for hedging unexpected changes in volatility. Although pricing volatility derivatives demands extreme care in modeling the underlying volatility process, not much attention has been devoted to the complete specification of the autonomous process that volatility follows in continuous time. Despite the fact that jumps are widely co...