Merton’s Jump Diffusion Model an Application to Stock Markets of East African Countries

Novat, Kimaro; Charles, W. M.; Masanja, Verdiana Grace

doi:10.31695/ijasre.2019.33454

Cited by 4 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, the jump-diffusion models have been used widely to describe the underlying assets in the real financial market. For real examples, see [28][29][30]. We derive the pricing formula of power exchange options with credit risk when the underlying assets follow jump-diffusion models in the next section.…”

Section: Modelmentioning

confidence: 99%

Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model

Jeon

Kim

2021

Mathematics

View full text Add to dashboard Cite

In this paper, we study the valuation of power exchange options with a correlated hybrid credit risk when the underlying assets follow the jump-diffusion processes. The hybrid credit risk model is constructed using two credit risk models (the reduced-form model and the structural model), and the jump-diffusion processes are proposed based on the assumptions of Merton. We assume that the dynamics of underlying assets have correlated continuous terms as well as idiosyncratic and common jump terms. Under the proposed model, we derive the explicit pricing formula of the power exchange option using the measure change technique with multidimensional Girsanov’s theorem. Finally, the formula is presented as the normal cumulative functions and the infinite sums.

show abstract

Section: Modelmentioning

confidence: 99%

Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model

Jeon

Kim

2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…Ruf and Scherer [17] discussed valuing of a corporate bond and how stochastic recovery rates are modelled using the model. Novat et al [16] applied Merton's jump-diffusion model to stock market by considering certain stocks of three East African countries. Salmi and Toivanen [18] discussed an iterative procedure for valuing American options driven by jump-diffusion processes, while Wang et al [20] discussed valuation of vulnerable American options driven by such processes.…”

Section: Introductionmentioning

confidence: 99%

Jump-Diffusion Process of Interest Rates and the Malliavin Calculus

Udoye¹,

Ogbogbo²,

Akinola³

2021

Int. J. of Appl. Math.

View full text Add to dashboard Cite

In this paper, we employ the existing Hull-White short rate model to derive an interest rate model driven by jump-diffusion process. Interest rates experience both positive and negative jumps at some intervals as a result of several factors which include natural disasters and presence of pandemics such as corona virus. Much has been done in the modelling of interest rates driven by Brownian motion process whereas little emphasis are laid on jumps inherent in the interest rates. For efficient modelling and pricing of financial derivatives, there is need to consider the aspect of jumps. Hence, this paper bridges the gap by focusing on an improved model. Sensitivities namely 'delta', 'vega', 'Theta' and 'Gamma' of the new model are also derived using Malliavin calculus.

show abstract

“…Lau et al (2019) presented an approach to estimate market parameters modelled using a certain jump-diffusion model. Novat et al (2019) discussed Merton's jump-diffusion model in stock markets of three East African countries. Salmi and Toivanen (2011) derived iterative steps for valuing American option using the model.…”

Section: Introductionmentioning

confidence: 99%

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

Udoye

Ogbaji

Akinola

et al. 2021

Annals of Science and Technology

View full text Add to dashboard Cite

Interest rate paths experience discontinuities in the presence of certain factors. Much of the work on interest rate modelling has no consideration for effects of such unexpected occurrences in real life. A good risk manager needs to have a better model that considers possibility of unexpected occurrences. In this paper, we discuss step by step extension of Vasicek model to both jump model and jumpdiffusion model using Itô’s formula as the major tool. We also derive the greeks ‘delta’ and ‘vega’ that measure sensitivity of the interest rate with respect to both changes in its initial interest rate and volatility in an interbank rate.

show abstract

Merton’s Jump Diffusion Model an Application to Stock Markets of East African Countries

Cited by 4 publications

References 0 publications

Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model

Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model

Jump-Diffusion Process of Interest Rates and the Malliavin Calculus

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

Contact Info

Product

Resources

About