A model is developed for evaluating the conditional probability of hitting an upper barrier before a lower barrier, and vice versa, for a tied down geometric Brownian motion with drift. The method produces an analytical value for this probability, assuming that the barrier levels are constant and continuously monitored.

Abstract

Entrepreneurs are the moving force of economic growth. Through entrepreneurship comes employment opportunities. From the Filipino youth to Filipino women and up to Filipino professional, there is always that profound intention to engage themselves in entrepreneurship not just to generate revenue but also to help in the upliftment of…[Read more]

This article presents a model for pricing complex CDO structures and compute the sensitivities of the risk factors. The complex CDO structures need to be priced using the market information on tranche losses at multiple points of time. Currently, the model is being used for the valuation of forward starting CDO trades (FSCDO) and loss-trigger…[Read more]

The structure of a Binary Return Note is similar to the one of a regular note, but the coupons are
contingent on return rates on stocks. Quasi-Monte Carlo simulation is used for pricing the product.

We present a pricing model for fade option. A fade option can be more precisely named as “point-barrier option”. The fade option is a vanilla option that exists or dies if a barrier is breached on a single preset date, which is prior or equal to the contract maturity.

Average rate or Asian options have a payoff function proportional to an average rate or price. The average price is calculated over a sampling of specified dates that need not be equally spaced in time. The average price or rate tends to be less volatile than a single underlying price and hence, an option on the underlying average price should be…[Read more]

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]

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]