VIX futures and option are the most popular contracts traded in the Chicago Board Options Exchange. The bid-ask spreads of traded VIX derivatives remain to be wide, possibly due to lack of reliable pricing models. In this paper, we consider pricing VIX derivatives under the consistent model...

Reset clauses on the strike price and maturity date are commonly found in derivative contracts, like insurance segregated funds, bonds and executive warrants. We analyze the optimal reset policy adopted by the holder of an option that possesses the reset rights on the strike price and date of...

The reload provision in an employee stock option entitles its holder to receive one new (reload) option from the employer for each share tendered as payment of strike upon the exercise of the stock option. The number of reloads allowed can be finite or infinite. The shout feature in a call...

A knock-in American option under a trigger clause is an option contract in which the option holder receives an American option conditional on the underlying asset price breaching certain trigger level (or called barrier level). We present closed form valuation formulas for knock-in American...

We develop a singular stochastic control model for pricing variable annuities with the guaranteed minimum withdrawal benefit. This benefit promises to return the entire initial investment, with withdrawals spread over the term of the contract, irrespective of the market performance of the...

1. Volatility Trading and Variance Derivatives. 1.1. Implied Volatility and Local Volatility. 1.2. Volatility Trading using Options. 1.3. Derivatives on Discrete Realized Variance. 1.4. Replication of Variance Swaps. 1.5. Practical Implementation of Replication: Finite Strikes and Discrete...