A variance/volatility swap is an instrument that allows explicit exposure to the realized variance/volatility of an index, stock, etc., without exposure to other risks commonly encountered with derivatives: delta, gamma, etc.

We review the equity forward and futures pricing models. Consider an index level, I, at a future time, T. With respect to I, we calculate 1) the forward price, 2) the futures price, and 3) delta.

A valuation model is presented to calculate price, hedge ratio, and implied volatility for forward starting European calls and puts. The model focuses on the numerical accuracy of the implementation.

The model calculates numbers that characterize the effect of adding an extra instrument to a portfolio of loan commitments. To be useful, these numbers should be additive with respect to the facilities making up the portfolio, so that their total would have the same meaning for the portfolio as each individual number has for the respective…[Read more]

Equity value at risk (VaR) model requires implied volatilities with respect to various indices and maturities, which range from three months to five years. A model is presented for generating a term-structure of implied equity index volatilities for use in calculating VaR.

A model is used to price a derivative whose payoff depends on returns over N periods on a shrinking basket of originally N assets. Each period, the worst return is added to the cumulative sum after being capped and floored, and the corresponding asset removed from the basket (hence a shrinking basket). The cap and floor rates are given for each…[Read more]

Credit value at risk (VaR) is used for measuring and analyzing credit risk of a portfolio. The basic methodology of the Credit VaR employs the credit migration approach spearheaded by RiskMetrics. It assumes that obligor’s credit quality is determined by the obligor’s asset value, which in turn is approximated by its standardized equity return.

We present a model for pricing a credit derivative product where party A has sold default put protection on a Euro denominated bond. Specifically, upon bond issuer default, party A must pay to party B a notional amount of 10 million USD (excluding accrued interest). In exchange, party B must pay a fixed rate to party A, on a quarterly basis,…[Read more]

We present a valuation model for pricing a gold derivatives trade. The trade can be structured to synthesize a typical gold-miner’s hedge, specifically, a swap in which one party receives long-term interest rates and pays a blend of short-term interest rates and short-term gold lease rates.

We present a model for pricing a path-dependent, equity-linked payoff. Here a bounded price return is calculated from an underlying index at certain pre-specified dates. The total return at maturity is given by the sum of the bounded price returns above, but where a specified number of the highest of these returns are set to a cap value.

A model is presented for pricing an American call option on stock. The option tenor is n years, and its strike price is increased every anniversary. It has also the following feature: if the stock price stays in excess of 200% of the current strike price during 10 consecutive trading days. The seller can issue a notice to the buyer that one half…[Read more]

We present a valuation model for pricing two asset barrier options on commodity futures. Applications to commodity futures have a number of specific. The analytical valuation formulas are also implemented. The payoff of a two asset barrier options is made against one of the assets, while the other asset is used to trigger the barrier.