Term structure movements implicit in Asian option prices

Almeida, Caio; Vicente, José Valentim Machado

doi:10.1080/14697681003720253

Cited by 9 publications

(4 citation statements)

References 34 publications

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“…al (1992)) to price IDI options. Almeida and Vicente (2012) implemented a Gaussian model to study the movements of the term structure of the interest rates. Finally, Genaro and Avellaneda ( 2018) extend a Gaussian model with jumps at deterministic times.…”

Section: Analytical Resultsmentioning

confidence: 99%

Hedging Interest Rate Options with Reinforcement Learning: an investigation of a heavy-tailed distribution

Da Silva,

Baczynski,

De Mello

2023

BMS

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Purpose: The study intends to model an interest rate index option using a heavy-tailed distribution. The goal is to calculate the interest rate path-dependent option prices that are consistent with market data and to develop a reinforcement learning strategy to discretely hedge the position considering transaction costs. Methodology: This paper presents a mathematical framework to calculate the price of interest rate path-dependent options. The research adapted a Fourier cosine series formula to employ the characteristic function of the present value of the forward index, which is modeled as a variance-gamma process and uses deep Q-learning to hedge such options. Findings: There is market evidence that the implied volatility curve is not flat. The study demonstrated that the variance-gamma process generates an increasing volatility smile, which is consistent with market observations. Additionally, hedging results show that the path-dependent options generated from the variance-gamma process can be efficiently hedged with advanced Q-learning techniques. Research limitations/implications: The study comprised only the variance-gamma process. Other probability distributions, such as the Normal Inverse Gaussian model, should be investigated. Practical implications: This study reveals which type of probability distribution should be present in a pricing engine to be consistent with implied volatilities. The approach provided here can assist managers in evaluating and comprehending market pricing behavior as well as achieving discrete hedging with costs. Originality: The paper addressed the merging of a fast pricing method for the interest rate options with a heavy-tailed distribution and the discrete interest rate derivatives hedging with reinforcement learning.

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Section: Analytical Resultsmentioning

confidence: 99%

Hedging Interest Rate Options with Reinforcement Learning: an investigation of a heavy-tailed distribution

Da Silva,

Baczynski,

De Mello

2023

BMS

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“…Notably, our approach differs from traditional models, such as those of Vasicek (1977) and Almeida and Vicente (2012), or the more general models of Bouziane (2008), as it accounts for scheduled events that occur and impact interest rate products. Our model also differs from that of Heidari and Wu (2009) because we account for the discrete nature of interest rate jumps.…”

Section: Discussionmentioning

confidence: 99%

Discretely Distributed Scheduled Jumps and Interest Rate Derivatives: Pricing in the Context of Central Bank Actions

da Silva,

Baczynski

2024

Economies

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Interest rate dynamics are influenced by various economic factors, and central bank meetings play a crucial role concerning this subject matter. This study introduces a novel approach to modeling interest rates, focusing on the impact of central banks’ scheduled interventions and their implications for pricing bonds and path-dependent derivatives. We utilize a modified Skellam probability distribution to address the discrete nature of scheduled interest rate jumps and combine them with affine jump-diffusions (AJDs) in order to realistically represent interest rates. We name this class the AJD–Skellam models. Within this class, we provide closed-form formulas for the characteristic functions of a still broad class of interest rate models. The AJD–Skellam models are well-suited for using the interest rate version of the Fourier-cosine series (COS) method for fast and efficient interest rate derivative pricing. Our methodology incorporates this method. The results obtained in the paper demonstrate enhanced accuracy in capturing market behaviors and in pricing interest rate products compared to traditional diffusion models with random jumps. Furthermore, we highlight the applicability of the model to risk management and its potential for broader financial analysis.

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“…In my simple model I have a close-form expression for y m . According to Almeida and Vicente (2012):…”

Section: Modelmentioning

confidence: 99%

A non-knotty inflation risk premium model

Vicente

2022

Applied Economics

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In this paper I estimate the inflation risk premium (IRP) using a low-dimensional arbitragefree dynamic model through a novel strategy. Instead of modeling the nominal and real yields jointly, I make assumptions about the short-term inflation rate. More specifically, I assume it follows a Gaussian process. This framework has a closed-form expression for IRP. Since inflation yields are not observed, to estimate the model parameters I approximate them by the break-even inflation rate. This approximation works well because the convexity correction is very small. I find the estimated IRP is strongly correlated with those obtained using surveys or more complex models. Therefore, I provide an easier procedure to obtain IRP, avoiding the cumbersome estimation process of high-order models.

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Term structure movements implicit in Asian option prices

Cited by 9 publications

References 34 publications

Hedging Interest Rate Options with Reinforcement Learning: an investigation of a heavy-tailed distribution

Hedging Interest Rate Options with Reinforcement Learning: an investigation of a heavy-tailed distribution

Discretely Distributed Scheduled Jumps and Interest Rate Derivatives: Pricing in the Context of Central Bank Actions

A non-knotty inflation risk premium model

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