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Introduction to Variance Swaps
The purpose of this article is to introduce the properties of variance swaps, and give insights into the hedging and valuation of these instruments from the particular lens of an option trader.
Tue 7 Dec 2021
Monte Carlo in Esperanto
This article shows how a simple parser environment in Excel/VBA could be used to perform single and multi-dimensional Monte Carlo.
Thu 4 Nov 2021
Numerical Methods for the Markov Functional Model
Some numerical methods for efficient implementation of the 1- and 2-factor Markov Functional models of interest rate derivatives are proposed.
Thu 4 Nov 2021
Order Statistics for Value at Risk Estimation and Option Pricing
We apply order statistics to the setting of VaR estimation. Here techniques like historical and Monte Carlo simulation rely on using the k-th heaviest loss to estimate the quantile of the profit and loss distribution of a portfolio of assets. We show that when the k-th heaviest loss is used the expected quantile and its error will be independent of the portfolio composition and the return functions of the assets in the portfolio.
Tue 12 Oct 2021
Pricing Rainbow Options
A previous paper (West 2005) tackled the issue of calculating accurate uni-, bi- and trivariate normal probabilities. This has important applications in the pricing of multiasset options, e.g. rainbow options. In this paper, we derive the Black—Scholes prices of several styles of (multi-asset) rainbow options using change-of-numeraire machinery. Hedging issues and deviations from the Black-Scholes pricing model are also briefly considered.
Tue 12 Oct 2021
Finformatics: How to Measure Really Small Things
The orthodoxy has tendency to ignore drift which leaves opportunity for finformaticians the market over…
Wed 15 Sep 2021
A VaR-based Model for the Yield Curve
An intuitive model for the yield curve, based on the notion of value-at-risk, is presented. It leads to interest rates that hedge against potential losses incurred from holding an underlying risky security until maturity. This result is also shown to tie in directly with the Capital Asset Pricing Model via the Sharpe Ratio. The conclusion here is that the normal yield curve can be characterised by a constant Sharpe Ratio, non-dimensionalised with respect to √T, where T is the bond maturity.
Wed 15 Sep 2021
Life Settlements and Viaticals
Life settlements and viaticals are contracts associated with death. Life settlements are a secondary market for the life insurance policies held by individuals. These individuals may, typically later in life, want to sell their policy. The policy is usually worth a lot more than its surrender value. Many of these life insurance policies are then usually packaged together and sold as one product. To the quant, the question is how to model and price, and hedge, individual policies and portfolios of policies.
Thu 5 Aug 2021
Valuation of American Call Options
The purpose of this paper is to provide an analytical solution for American call options assuming proportional dividends. Proportional dividends are more realistic for long-term options than absolute dividends and the formula does not have the flaws known from absolute dividend formulae.
Thu 5 Aug 2021
Poker as a Lottery
Doyle Brunson, two-time winner of the World Series of Poker main event, has likened a poker tournament to a lottery in which more skilled players (like himself) hold more tickets than less skilled players. This article works out the details of this analogy and provides some very general and very important results for anyone hoping to be a winning poker player.
Thu 8 Jul 2021
