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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
A Conditional Valuation Approach for Path-Dependent Instruments
This paper focuses on the methodology for calculating the potential future exposure of path-dependent derivative instruments.
Thu 8 Jul 2021
Scenarios IV: Planning for Disasters and then Dealing with them
In the aftermath of Katrina, Bill Ziemba discusses planning for the economic and financial effects of natural disasters.
Tue 22 Jun 2021
Monte Carlo Methods in Quantitative Finance Generic and Efficient MC Solver in C++
This paper describes how the authors have designed and implemented a software architecture in C++ to model one-factor and multifactor option pricing problems.
Tue 22 Jun 2021
A Generalised Procedure for Locating the Optimal Capital Structure
This article presents a generalisation of an earlier approach for determining and locating the optimal capital structure of a corporate firm.
Thu 8 Apr 2021
Six Degrees of Idiocy
One of the classic works of poker, and risk management, is Herbert Yardley’s 1957 best-seller 'The Education of a Poker Player, Including Where and How One Learns to Win'. Aaron Brown explores how in both poker and finance an individual’s strategic idiocy can be quantified and analyzed.
Thu 8 Apr 2021
Not-so-Complex Logarithms in the Heston Model
In Heston’s stochastic volatility framework [Heston 1993], semi-analytical formulæ for plain vanilla option prices can be derived. Unfortunately, these formulæ require the evaluation of logarithms with complex arguments during the involved inverse Fourier integration step. In this article, a new approach is proposed to solve this problem which enables the use of Heston’s analytics for practically all levels of parameters and even maturities of many decades.
Fri 5 Mar 2021
