Forecasting the elasticity of variance with LSTM recurrent neural networks

A Mellin transform approach to pricing barrier options under stochastic elasticity of variance

“…Since the formula for the barrier option price obtained in this article is given in terms of the Black–Scholes price, its implementation would be easy from the industrial application point of view. On the other hand, a recent study by Kim and Kim 17 finds that the SEV model can capture a unique feature of the culmination of financial market crisis caused by the recent COVID‐19 pandemic outbreak. This suggests that derivatives pricing based on the SEV model would be a preferred choice for investigating the financial crisis impact on the prices since our pricing formula is given as an expansion in powers of the characteristic amplitude scale and variation time of the SEV.…”

“…Appendix E) leading to a lot slower computation of the option price. This is due to the existence of an inhomogeneous term in (17). So, we split the problem into two parts.…”

“… 0,0 (t, s) is the same as P 0,0 (t, s) in (14) but defined over the extended domain s > 0. Moreover, the restriction of  1,0 (t, s) to the interval s > B is the solution of the PDE problem(17) for P 1,0 (t, s). Precisely, P 1,0 (t, s) is given byP 1,0 (t, s) = 𝜎 2 ⟨f ⟩ ∫ ′ , s; T, 𝜉) log(𝜉) 𝜉 2 𝜕 2  0,0 (t ′ , 𝜉) 𝜕𝜉 2 d𝜉dt ′ ,where g is the transition density function corresponding to  20 and it is given by g(t ′ , s; T, 𝜉) = 1…”