On the Qualitative Effect of Volatility and Duration on Prices of Asian Options

Hedging of Asian options under exponential Lévy models: computation and performance

“…We note that the vega of the given contract is always positive (see Equation 17), which extends the findings of Carr et al (2008) to the case of a discretely monitored arithmetic Asian option.…”

“…Assuming a generic process with independent increments for the log-returns of the underlying, we prove that differentiation under the integral sign with respect to parameters of interest is permissible. In particular, we reach general solutions for the option's delta and gamma (Theorem 1), but also the non-trivial case of the option's vega for a lognormal underlying (Theorem 2); en route, we prove that the vega of the given contract is positive, extending the results of Carr et al (2008) from the case of a continuously to a discretely monitored arithmetic Asian option. It is worth pointing out that the suggested method can give access to any other price sensitivity, providing that differentiation under the integral sign is allowed.…”

Asian and Australian options: A common perspective

“…where for the second equality we used the substitution t → T − t and for the third equality Equation (5). Clearly, the integrand on the right hand side satisfies the stochastic differential equation…”

“…We also show how the Milevsky and Posner (1998) result on the reciprocal Γ-approximation for Asian options can be quickly obtained by using the connection to Australian options. Further, we present an analytical (exact) pricing formula for Australian options and adapt a result of Carr, Ewald and Xiao (2008) to show that the price of an Australian call option is increasing in the volatility and by doing this answering a standing question by Moreno and Navas (2008). …”

Pricing and Hedging of Asian Options: Quasi-Explicit Solutions via Malliavin Calculus

“…We do not provide an expression for the vega of an Asian option here, but refer to Carr, Ewald, and Xiao [3] instead for an interesting result on the volatility dependence of Asian option prices.…”