The historical returns on equity index options are well known to be strikingly negative. That is typically explained either by investors having convex marginal utility over stock returns (e.g. crash/variance aversion) or by intermediaries demanding a premium for hedging risk. This paper examines...

At each maturity a discrete return distribution is inferred from option prices. Option pricing models imply a comparable theoretical distribution. As both the transformed data and the option pricing model deliver points on a simplex, the data is statistically modeled by a Dirichlet distribution...

I derive closed-form expressions for the value of American call and put options (on an asset with continuous yield) using the Feynman-Kac formula, modelling the size of early exercise premium as a function of the strike, dividend yield and time to maturity. Strategies involving European options...

This paper improves continuous-time variance swap approximation formulas to derive exact returns on benchmark VIX option portfolios. The new methodology preserves the variance swap interpretation that decomposes returns into realized variance and option implied-variance.We apply this new...

The fair value of an option is given by breakeven volatility, the value of implied volatility that sets the profit and loss of a delta-hedged option to zero. We calculate breakeven volatility for 400,000 options traded on the S&P 500 Index, and we build a predictive model for these volatility...

Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a small-time asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the...

In this paper, we derive optimal hedging strategies for options in electricity futures markets. Optimality is measured in terms of minimal variance and the associated minimal variance hedging portfolios are obtained by a stochastic maximum principle. Our explicit results are particularly useful...

This paper has proposed new option Greeks and new upper and lower bounds for European and American options. It shows that because of the put-call parity, the Greeks of put and call options are interconnected and should be shown simultaneously. In terms of the theory of the firm, it is found that...

I propose a simple generalization of put-call parity that holds for a large class of exotic European options. The result rests on a reasonable generalization of the concepts of put and call. The proof is based on the fundamental theorem of arbitrage pricing and elementary properties of real...

Option pricing models based on an underlying lognormal distribution typically exhibit volatility smiles or smirks where the implied volatility varies by strike price. To adequately model the underlying distribution, a less restrictive model is needed. A relaxed binomial model is developed here...