In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian sesame price fluctuations. The White Humera Gondar Sesame Grade 3 (WHGS3) price, which is recorded from 5 November 2010 to 30 March 2018 at Ethiopia Commodity Exchange (ECX) market, is used to analyze the price fluctuation. The nature of log-returns of the price is asymmetric (positively skewed) and exhibits high kurtosis. We used Jump diffusion models for modeling and option pricing of sesame price. The method of maximum likelihood is applied to estimate the parameters of the models. We used the Root Mean Square Error (RMSE) to test the goodness of fitting for the two models to the data. This test indicates that the models fit the data well. The techniques of analytical and Monte Carlo simulation are used to find the call option pricing of WHGS3 sesame price. From the results, we concluded that Double Exponential Jump diffusion (DEJD) model is more efficient than Merton’ s model for modeling and option pricing of this sesame price.

We consider the hedging problem in a Jump-diffusion market with correlated assets. For this purpose, we employ the locally risk minimizing approach and obtain the hedging portfolio as a solution of a multidimensional system of linear equations. This system shows that in a continuous market, independence and correlation assumptions of assets lead to the same locally risk minimizing portfolio. In addition, we investigate the sensitivity of the risk with respect to the variation of correlation parameters, this enables us to select the more profitable portfolio. The results show that the risk increases, with increasing the correlation parameters. This means that to reduce risk it is necessary to invest in low correlated assets.

The Black-Scholes model assumes that the price of the underlying asset follows a geometric Brownian motion. This assumption has two implications: first, log-returns over any horizon are normally distributed with constant volatility σ and the second, stock price evolution is continuous, therefore, there is no market gaps. These conditions are commonly violated in practice: empirical returns typically exhibit fatter tails than a normal distribution, volatility is not constant over time, and markets do sometimes gap. The existence of volatility skew will misprice options price. Derived from these flaws, a number of models have proposed. In this paper we will analyze, simulate and compare two most important models which have widespread using: Jump diffusion model and stochastic volatility model. Each of the aforementioned models have programmed in MATLAB and Python, then their results have been compared together in order to provide a robust understanding of each of them. Our results show that in comparison to Black-Scholes model these two models yield better performance.

The stochastic reaction diffusion systems may suffer sudden shocks, in order to explain this phenomena, we use Markovian Jumps to model stochastic reaction diffusion systems. In this paper, we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian Jumps. Under some reasonable conditions, we show that the trivial solution of stochastic reaction diffusion systems with Markovian Jumps is almost surely exponentially stable. An example is given to illustrate the theory.

Given the significant benefits of the Radial Basis Function (RBF) approach, here in this paper, we tried to exploit and adopt this method for the Fixed-Rate Mortgage (FRM) models. In the real world, a Jump occurs due to an unknown reason and perhaps better reflects the evolution of real estate prices during bubbles and crises in the real estate markets. For the house price evolution, the Jump- diffusion models are used which would lead to a Partial-Integro Differential Equation (PIDE) model. The main concentration is on the difficulty of projecting the pricing of FRM that deals with contracts in where the underlying stochastic factors are the house price and the interest rate. Utilizing the stochastic house-price and stochastic interest-rate models, we were able to develop a reliable mortgage valuation. The identified Partial-Integro Differential Equation (PIDE) from the FRM pricing model, solved by RBF considering the fact that a closed-form solution is usually unavailable. Further, to display the expected behaviour of the contract, the possible applications of the suggested method applied to UK fixed-rate mortgages. Based on available resources, a set of economic parameters was determined for the mortgage to provide an instance to show the applicability of the proposed approach.

In this paper, we derive a new Jump-diffusion model for electricity spot price from the “ Price-Cap” principle. Next, we show that the model has a non-classical mean-reverting linear drift. Moreover, using this model, we compute a new exact formula for the price of forward contract under an equivalent martingale measure and we compare it to Cartea et al. (Appl Math Finance 12(4): 313– 335, 2005) formula.