Ioannis Kyriakou

An improved convolution algorithm for discretely sampled Asian options

We suggest an improved FFT pricing algorithm for discretely sampled Asian options with general independently distributed returns in the underlying. Our work complements the studies of Carverhill and Clewlow [Risk, 1990, 3(4), 25-29], Benhamou [J. Comput. Finance, 2002, 6(1), 49-68], and Fusai and Meucci [J. Bank. Finance, 2008, 32(10), 2076-2088], and, if we restrict our attention only to log-normally distributed returns, also Vecer [Risk, 2002, 15(6), 113-116]. While the existing convolution algorithms compute the density of the underlying state variable by moving forward on a suitably defined state space grid, our new algorithm uses backward price convolution, which resembles classical lattice pricing algorithms. For the first time in the literature we provide an analytical upper bound for the pricing error caused by the truncation of the state space grid and by the curtailment of the integration range. We highlight the benefits of the new scheme and benchmark its performance against existing finite difference, Monte Carlo, and forward density convolution algorithms.

General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options

We propose an accurate method for pricing arithmetic Asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation. In particular, we derive analytical expressions for the lower bound in the Fourier domain. This is then recovered by a single univariate inversion and sharpened using an optimization technique. In addition, we derive an upper bound to the error from the lower bound price approximation. Our proposed method can be applied to computing the prices and price sensitivities of Asian options with fixed or floating strike price, discrete or continuous averaging, under a wide range of stochastic dynamic models, including exponential Levy models, stochastic volatility models, and the constant elasticity of variance diffusion. Our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases.

Convertible bond valuation in a jump diffusion setting with stochastic interest rates

This paper proposes an integrated pricing framework for convertible bonds, which comprises firm value evolving as an exponential jump diffusion, correlated stochastic interest rates movements and an efficient numerical pricing scheme. By construction, the proposed stochastic model fits in the framework of affine jump diffusion processes of Duffie et al. [Econometrica, 2000, 68, 1343–1376] with tractable behaviour. We define the firm’s optimal call policy and investigate its impact on the computed convertible bond prices. We illustrate the performance of the numerical scheme and highlight the effects originated by the inclusion of jumps, stochastic interest rates and a non-zero correlation structure between firm value and interest rates.

Affine‐Structure Models and the Pricing of Energy Commodity Derivatives

We consider a seasonal mean-reverting model for energy commodity prices with jumps and Heston-type stochastic volatility, and three nested models for comparison. By exploiting the affine form of the log-spot models, we develop a general valuation framework for futures and discrete arithmetic Asian options. We investigate five major petroleum commodities from Europe (Brent crude oil, gasoil) and US (light sweet crude oil, gasoline, heating oil) and analyse the effects of the competing fitted spot models in futures pricing, Asian options pricing and hedging. We find evidence that price jumps and stochastic volatility are important features of the petroleum price dynamics.

Jumps and Stochastic Volatility in Crude Oil Prices and Advances in Average Option Pricing

Crude oil derivatives form an important part of the global derivatives market. In this paper, we focus on Asian options which are favoured by risk managers being effective and cost-saving hedging instruments. The paper has both empirical and theoretical contributions: we conduct an empirical analysis of the crude oil price dynamics and develop an accurate pricing set-up for arithmetic Asian options with discrete and continuous monitoring featuring stochastic volatility and discontinuous underlying asset price movements. Our theoretical contribution is applicable to various commodities exhibiting similar stylized properties. We here estimate the stochastic volatility model with price jumps as well as the nested model with omitted jumps to NYMEX WTI futures vanilla options. We find that price jumps and stochastic volatility are necessary to fit options. Despite the averaging effect, we show that Asian options remain sensitive to jump risk and that ignoring the discontinuities can lead to substantial mispricings.

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Levy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.

Communication and Personal Selection of Pension Saver’s Financial Risk

The paper shows how to reform the platform of pension products so that pension savers, professional financial advisors, actuaries and investment experts intuitively understand the underlying financial risk of the optimal investment profile. It is also pointed out that an excellent optimal investment strategy can destroy the future expected utility of a pension saver if the financial communication is wrong. It is shown that a simple system with an upper and a lower bound, originally inspired by Merton (2014), which can be executed easily using fintech, can replace complicated power utility optimization for the pension saver so that everyone can exactly understand the amount of financial risk taken. The paper focuses on investing money as a lump sum because being able to communicate the associated financial risk can serve as the first step towards communicating more complex pension saving structures.