tristan guillaume - Academia.edu (original) (raw)
Papers by tristan guillaume
Annals of Operations Research
Journal of Applied Mathematics and Physics
International Journal of Applied and Computational Mathematics
Annals of Operations Research
The Journal of Derivatives
ABSTRACT In this article, a general, flexible form of autocallable note is analytically valued, a... more ABSTRACT In this article, a general, flexible form of autocallable note is analytically valued, and its payoff profile and risk-management properties are discussed. The general autocallable structure under consideration includes the following features: regular coupons, reverse-convertible provision, down-and-out American barrier, best-of mechanism, and snowball effect. These features are more or less fully addressed according to the entailed valuation difficulties. Simpler notes are easily designed and priced on the basis of this general structure. The formulas provided in this article can be expected to be a valuable tool for both buyers and issuers in terms of risk management. Indeed, they enable investors to assess their chances of early redemption as well as their expected return on investment as a function of the contract's specifications, and they allow issuers to accurately and efficiently analyze and compute their various risk exposures.
Communications in Statistics - Simulation and Computation
Applied Mathematical Sciences
This paper presents exact analytical formulae for the crossing of a constant onesided or two-side... more This paper presents exact analytical formulae for the crossing of a constant onesided or two-sided boundary by a geometric Brownian motion with timedependent, non-random, drift and diffusion coefficients, under the assumption that the drift coefficient is a constant multiple of the diffusion coefficient, as well as approximate analytical formulae for general time-dependent, non-random, drift and diffusion coefficients and general time-dependent, non-random, boundaries. The numerical implementation of these formulae is very simple.
Journal of Probability and Statistics
This paper provides explicit formulae for the probability that an arithmetic or a geometric Brown... more This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasi-instantaneously and with utmost precision. The sensitivity of the survival probability to the number and the ordering of the steps in the boundary is analyzed.
ISRN Applied Mathematics
This paper provides new explicit results for some boundary crossing distributions in a multidimen... more This paper provides new explicit results for some boundary crossing distributions in a multidimensional geometric Brownian motion framework when the boundary is a piecewise constant function of time. Among their various possible applications, they enable accurate and efficient analytical valuation of a large number of option contracts traded in the financial markets belonging to the classes of barrier and look-back options.
The Journal of Derivatives
Double barrier options have been traded for a long time in the markets and they are embedded in a... more Double barrier options have been traded for a long time in the markets and they are embedded in a variety of popular structured products. However, in their standard form, they lack flexibility inasmuch as they feature a constant barrier level during the entire option life. Step double barrier options overcome this limitation by allowing investors to set the knockout or knock-in levels they want at the time of their choosing rather than by imposing an arbitrary mathematical form upon the time-varying double barrier. Although step double barrier options are actively traded, no analytical formula is known for their valuation and hedging. In this paper, not only regular step double barrier options are analytically valued, but also more exotic contracts combining periods with and without active barriers as well as step double barrier options written on several assets. Financial properties of these instruments are discussed in comparison with other existing contracts.
International Journal of Financial Engineering
In this paper, a general form of autocallable note is analytically valued, which includes the fol... more In this paper, a general form of autocallable note is analytically valued, which includes the following features: regular coupons, reverse convertible provision and possible participation in the growth of the underlying equity asset. Simpler notes can be designed and analytically priced on the basis of this general structure. The equity asset follows a jump-diffusion process, while interest rates are driven by a two-factor model. Equity and interest rate sources of randomness are correlated. The numerical implementation is easy and very efficient compared to alternative valuation techniques. The formula provided in this paper can thus be expected to be a valuable tool for both buyers and issuers in terms of pricing and risk management.
Journal of Applied Mathematics
This paper shows how to value multiasset options analytically in a modeling framework that combin... more This paper shows how to value multiasset options analytically in a modeling framework that combines both continuous and discontinuous variations in the underlying equity or foreign exchange processes and a stochastic, two-factor yield curve. All correlations are taken into account, between the factors driving the yield curve, between fixed income and equity as asset classes, and between the individual equity assets themselves. The valuation method is applied to three of the most popular two-asset options.
Http Dx Doi Org 10 1080 13504860210122384, Oct 14, 2010
ABSTRACT It is shown how to obtain explicit formulae for a variety of popular path-dependent cont... more ABSTRACT It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts with complex payoffs involving joint distributions of several extrema. More specifically, formulae are given for standard step-up and stepdown barrier options, as well as partial and outside step-up and step-down barrier options, between three and five dimensions. The proposed method can be extended to other exotic path-dependent payoffs as well as to higher dimensions. Numerical results show that the quasi-random integration of these formulae, involving multivariate distributions of correlated Gaussian random variables, provides option values more quickly and more accurately than Monte Carlo simulation.
Review of Derivatives Research, 2009
This paper extends the analytical valuation of options on the maximum or the minimum of several r... more This paper extends the analytical valuation of options on the maximum or the minimum of several risky assets in several directions. The first extension consists in including more assets in the payoff and making the latter more flexible by adding knock-in and knockout provisions. The second extension consists in pricing these contracts in a multivariate jump-diffusion framework allowing for a stochastic twofactor term structure of interest rates. In both cases, explicit formulae are provided which yield prices quasi instantaneously and with utmost precision. Hedge ratios can be easily and accurately derived from these formulae. Keywords Multiasset option • Rainbow option • Best-of option • Option on the maximum or the minimum • Dimension • Multivariate normal distribution 1 Introduction Multiasset options, or rainbow options, have been traded for a long time in the markets. Among this class of contracts, options on the best or the worst of several risky assets are popular. In its standard form, a European-style call on the maximum (the "best") of n assets provides the investor, at the option expiry, with the difference, if positive, between the highest of the n asset prices and a fixed strike price. Similarly, a put on the minimum (the "worst") provides the difference, if positive, between the strike price and the lowest of the underlying asset prices. It is not hard to see why these products appeal to investors. Indeed, they provide them with powerful tools of diversification. As such, they allow both to reduce their risk exposure and to expand their T. Guillaume (B)
Http Dx Doi Org 10 3905 Jod 2015 22 3 073, Feb 27, 2015
All the explicit formulae for the valuation of lookback and barrier options available in the fina... more All the explicit formulae for the valuation of lookback and barrier options available in the financial literature assume continuous monitoring of the underlying asset. In practice, however, monitoring is always discrete, and the gap between continuously and discretely monitored option values can be very large. In this paper, we provide explicit formulae for discretely monitored lookback and barrier options. They allow for non-constant volatility, interest rate, dividend rate and barrier parameters that vary as step functions of time. They can deal with any number and spacing of monitoring dates. They are not restricted to particular payoffs or strike price specifications. We also provide a simple rule for the numerical integration of these high-dimensional formulae, as well as an efficient interpolation method.
Review of Derivatives Research, 2003
This paper examines a path-dependent contingent claim called the window double barrier option, in... more This paper examines a path-dependent contingent claim called the window double barrier option, including standard but also more exotic features such as combinations of single and double barriers. Price properties and hedging issues are discussed, as well as financial applications.Explicit formulae are provided, along with simple techniques for theirimplementation. Numerical results show that they compare very favourablywith alternative pricing approaches
Annals of Operations Research
Journal of Applied Mathematics and Physics
International Journal of Applied and Computational Mathematics
Annals of Operations Research
The Journal of Derivatives
ABSTRACT In this article, a general, flexible form of autocallable note is analytically valued, a... more ABSTRACT In this article, a general, flexible form of autocallable note is analytically valued, and its payoff profile and risk-management properties are discussed. The general autocallable structure under consideration includes the following features: regular coupons, reverse-convertible provision, down-and-out American barrier, best-of mechanism, and snowball effect. These features are more or less fully addressed according to the entailed valuation difficulties. Simpler notes are easily designed and priced on the basis of this general structure. The formulas provided in this article can be expected to be a valuable tool for both buyers and issuers in terms of risk management. Indeed, they enable investors to assess their chances of early redemption as well as their expected return on investment as a function of the contract's specifications, and they allow issuers to accurately and efficiently analyze and compute their various risk exposures.
Communications in Statistics - Simulation and Computation
Applied Mathematical Sciences
This paper presents exact analytical formulae for the crossing of a constant onesided or two-side... more This paper presents exact analytical formulae for the crossing of a constant onesided or two-sided boundary by a geometric Brownian motion with timedependent, non-random, drift and diffusion coefficients, under the assumption that the drift coefficient is a constant multiple of the diffusion coefficient, as well as approximate analytical formulae for general time-dependent, non-random, drift and diffusion coefficients and general time-dependent, non-random, boundaries. The numerical implementation of these formulae is very simple.
Journal of Probability and Statistics
This paper provides explicit formulae for the probability that an arithmetic or a geometric Brown... more This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasi-instantaneously and with utmost precision. The sensitivity of the survival probability to the number and the ordering of the steps in the boundary is analyzed.
ISRN Applied Mathematics
This paper provides new explicit results for some boundary crossing distributions in a multidimen... more This paper provides new explicit results for some boundary crossing distributions in a multidimensional geometric Brownian motion framework when the boundary is a piecewise constant function of time. Among their various possible applications, they enable accurate and efficient analytical valuation of a large number of option contracts traded in the financial markets belonging to the classes of barrier and look-back options.
The Journal of Derivatives
Double barrier options have been traded for a long time in the markets and they are embedded in a... more Double barrier options have been traded for a long time in the markets and they are embedded in a variety of popular structured products. However, in their standard form, they lack flexibility inasmuch as they feature a constant barrier level during the entire option life. Step double barrier options overcome this limitation by allowing investors to set the knockout or knock-in levels they want at the time of their choosing rather than by imposing an arbitrary mathematical form upon the time-varying double barrier. Although step double barrier options are actively traded, no analytical formula is known for their valuation and hedging. In this paper, not only regular step double barrier options are analytically valued, but also more exotic contracts combining periods with and without active barriers as well as step double barrier options written on several assets. Financial properties of these instruments are discussed in comparison with other existing contracts.
International Journal of Financial Engineering
In this paper, a general form of autocallable note is analytically valued, which includes the fol... more In this paper, a general form of autocallable note is analytically valued, which includes the following features: regular coupons, reverse convertible provision and possible participation in the growth of the underlying equity asset. Simpler notes can be designed and analytically priced on the basis of this general structure. The equity asset follows a jump-diffusion process, while interest rates are driven by a two-factor model. Equity and interest rate sources of randomness are correlated. The numerical implementation is easy and very efficient compared to alternative valuation techniques. The formula provided in this paper can thus be expected to be a valuable tool for both buyers and issuers in terms of pricing and risk management.
Journal of Applied Mathematics
This paper shows how to value multiasset options analytically in a modeling framework that combin... more This paper shows how to value multiasset options analytically in a modeling framework that combines both continuous and discontinuous variations in the underlying equity or foreign exchange processes and a stochastic, two-factor yield curve. All correlations are taken into account, between the factors driving the yield curve, between fixed income and equity as asset classes, and between the individual equity assets themselves. The valuation method is applied to three of the most popular two-asset options.
Http Dx Doi Org 10 1080 13504860210122384, Oct 14, 2010
ABSTRACT It is shown how to obtain explicit formulae for a variety of popular path-dependent cont... more ABSTRACT It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts with complex payoffs involving joint distributions of several extrema. More specifically, formulae are given for standard step-up and stepdown barrier options, as well as partial and outside step-up and step-down barrier options, between three and five dimensions. The proposed method can be extended to other exotic path-dependent payoffs as well as to higher dimensions. Numerical results show that the quasi-random integration of these formulae, involving multivariate distributions of correlated Gaussian random variables, provides option values more quickly and more accurately than Monte Carlo simulation.
Review of Derivatives Research, 2009
This paper extends the analytical valuation of options on the maximum or the minimum of several r... more This paper extends the analytical valuation of options on the maximum or the minimum of several risky assets in several directions. The first extension consists in including more assets in the payoff and making the latter more flexible by adding knock-in and knockout provisions. The second extension consists in pricing these contracts in a multivariate jump-diffusion framework allowing for a stochastic twofactor term structure of interest rates. In both cases, explicit formulae are provided which yield prices quasi instantaneously and with utmost precision. Hedge ratios can be easily and accurately derived from these formulae. Keywords Multiasset option • Rainbow option • Best-of option • Option on the maximum or the minimum • Dimension • Multivariate normal distribution 1 Introduction Multiasset options, or rainbow options, have been traded for a long time in the markets. Among this class of contracts, options on the best or the worst of several risky assets are popular. In its standard form, a European-style call on the maximum (the "best") of n assets provides the investor, at the option expiry, with the difference, if positive, between the highest of the n asset prices and a fixed strike price. Similarly, a put on the minimum (the "worst") provides the difference, if positive, between the strike price and the lowest of the underlying asset prices. It is not hard to see why these products appeal to investors. Indeed, they provide them with powerful tools of diversification. As such, they allow both to reduce their risk exposure and to expand their T. Guillaume (B)
Http Dx Doi Org 10 3905 Jod 2015 22 3 073, Feb 27, 2015
All the explicit formulae for the valuation of lookback and barrier options available in the fina... more All the explicit formulae for the valuation of lookback and barrier options available in the financial literature assume continuous monitoring of the underlying asset. In practice, however, monitoring is always discrete, and the gap between continuously and discretely monitored option values can be very large. In this paper, we provide explicit formulae for discretely monitored lookback and barrier options. They allow for non-constant volatility, interest rate, dividend rate and barrier parameters that vary as step functions of time. They can deal with any number and spacing of monitoring dates. They are not restricted to particular payoffs or strike price specifications. We also provide a simple rule for the numerical integration of these high-dimensional formulae, as well as an efficient interpolation method.
Review of Derivatives Research, 2003
This paper examines a path-dependent contingent claim called the window double barrier option, in... more This paper examines a path-dependent contingent claim called the window double barrier option, including standard but also more exotic features such as combinations of single and double barriers. Price properties and hedging issues are discussed, as well as financial applications.Explicit formulae are provided, along with simple techniques for theirimplementation. Numerical results show that they compare very favourablywith alternative pricing approaches