The article discusses valuation models for the following products: power financial indices swap contracts (PWR-SWAP), power financial transmission rights contracts (PWRSWAP- FTR), power physical delivery contracts (PWR-PHYS) and power physical transmission contracts (PWR-TR-SPREAD). All products have similar valuation structure – index swap (or s…[Read more]

We offer a hybrid (trinomial tree plus semi-analytic formulas) pricing method for FX Double Window Double Barrier option . Currently, the model uses spot implied volatility for the first time window, and forward implied volatility for the second time window. These are Black-Scholes implied volatilities from traded vanilla European options, but,…[Read more]

The purpose of the model is to calculate the credit spread sensitivity, correlation sensitivity, and default sensitivity via analytic methods for index CDO trades and bespoke CDO trades. The credit spread sensitivity is defined as the change in the MTM by perturbing the credit spread by a small amount; the default sensitivity is calculated by…[Read more]

This paper was presented at “Encounters with the Uncanny in Education” seminar organized by Antti Saari, Jan Varpanen, and Johanna Kallio at University of Tampere. The seminar was part of their EnAct – Researching Environmental Activism and Self-Cultivation research project.

A pricing model for capped-accumulated-return-call (CARC) with volatility surface is presented. Proprietary approaches to interpreting volatility surface are employed during pricing. To accelerate the convergence when low discrepancy sequences are used in Monte Carlo simulation (Quasi-Monte Carlo simulation), the Brownian Bridge Path…[Read more]

The model serves the purpose of computing basis adjustments for credit spread curves of the constituent obligors of the indexes such that the market price of the index can be repriced exactly. These adjusted index constituent curves are then used to compute index base correlations and mapped base correlations for bespoke trades, price the standard…[Read more]

The payoff of reverse convertible product involves returns on multiple assets and is conditional on hitting of continuous barriers. The Monte Carlo methodology employed by ESP is an efficient conditioning technique.

Accounting requires the ability to forecast conduit administration fees. a simple stationary lognormal model for the fees is presented. Initially, the stationarity of the sweep fees is tested by measuring the level of mean reversion. Using a Dickey-Fuller statistical test the conduits are checked for approximate stationarity. Next, assuming the…[Read more]

The article presents a model for pricing digital-type barrier options on baskets of equity stocks. Within each payment period, there is a series of basket observation times. If at each observation time we observe that all basket constituent stocks remain between their lower and upper barriers, we receive a fixed coupon amount on the payment date…[Read more]

We present a model for pricing an exotic swap where one party receives a fixed amount and makes a series of variable payments at the end of each pre-defined calculation period. The variable payments can be modeled as Asian put option payoffs on the weighted sum of two respective commodity basket levels. Furthermore, each basket level consists of a…[Read more]

A model is present for pricing an Equity Asian Swap. One leg of the swap pays the return from a monthly average of the S&P TSE60 index less a constant strike. The payment from the other leg is similarly defined for a stock. The payments are tied to notional amounts that are specified according to two pre-determined monthly schedules. Most of the…[Read more]

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]