In this article, we consider the small-time asymptotics of options on a Leveraged Exchange-Traded Fund (LETF) when the underlying Exchange Traded Fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. Our main results are closed-form expressions for the leading order terms of off-the-money European call and put LETF option prices, near expiration, with explic...

This appendix provides additional intuition based on option pricing for the result in Proposition 2. Consider the case of monopoly. At time one, the monopolist is selling a series of call options, or equivalently units bundled with put options, rather than units themselves. The marginal price charged for a unit q at time two is simply the strike price of the option sold on unit q at time one. T...

We present an algorithm and its software implementation that computes implied volatilities for exchangetraded stock options. The LR (Leisen-Reimer) binomial tree is used for the underlying option pricing, which is adjusted for dollar cash dividends. The Brent’s method is used as the root-finding procedure. The option pricing procedure that is at the core of the root-finding is optimised to maxi...

It is common for firms to issue or purchase options on the firm’s own stock. Examples include convertible bonds, warrants, call options as employee compensation, and the sale of put options as part of share repurchase programs. This paper shows that option positions with implicit borrowing—such as put sales and call purchases—are tax-disadvantaged relative to the equivalent synthetic option wit...

In general, geometric additive models are incomplete and the perfect replication of derivatives, in the usual sense, is not possible. In this paper we complete the market by introducing the so-called power-jump assets. Using a static hedging formula, in order to relate call options and power-jump assets, we show that this market can also be completed by considering portfolios with a continuum o...