16 problems

The paper considers path-dependent functionals of a diffusion, including lookback and barrier options, whose expectations are approximated using an Euler scheme. Their weak discret…

Consider a time grid … For Bermudan option pricing, let the exercise dates be equidistant and coincide with time points in this grid. The option price is approximated using the Alm…

The Heston model is simulated using the Almost Exact Simulation (AES) scheme, which samples the variance process from its non-negative marginal distribution. European option-pricin…

Canonical-filtration conjecture. It should be enough to restrict the search for an optimal model to models equipped with the canonical filtration of the price process.

Let $R(z_0,z_1,z_2,0)$ be the stability function of the MCS scheme, and let $\theta=\tfrac{1}{3}$. For complex numbers $z_0,z_1,z_2$ satisfying … interpret $\gamma$ as a bound on t…

The paper considers option prices written on a continuous-time multiplicative semi-Markov process and, under suitable scaling, their convergence to the option price for an underlyi…

Consider an optimal trading strategy in the option-pricing model with transaction costs, depending on the time $t$ and stock price $S$. In the corresponding model without transacti…

Let $Q_j(t,y,S)$ satisfy the transaction-cost pricing equation … On the domain $[0,T]\times\mathbb{R}\times\mathbb{R}^{+}$, the equation divides the space into three regions. Davis…

Let a payoff function be well approximated by a quadratic polynomial, and consider the corresponding law of the solution in the rough Stein–Stein model and its Euler discretization…

Let Set1 be the parameter set considered in the numerical experiments, let the small region of interest (ROI) lie close to the early exercise region (EER), and let the option value…

Single-discretization conjecture. In practice, single discretization gives a good approximation for the expectation $\mathrm{E}f(S_T)$, better than double discretization or direct…

Let $D$ be a driftless diffusion with piecewise continuous local variance coefficient $a$, let $\Gamma$ be an independent unbiased gamma process, and define the subordinated proces…

Let $u(z,\tau;\lambda)$ be the solution represented by the heat-kernel formula above, with $\lambda_1>0$ fixed and $\lambda_2=\cdots=\lambda_N$ potentially approaching zero. Suppos…

Let $\psi$ be the Lévy exponent of the process under consideration, and let Condition denote the condition introduced earlier in the paper. Let the associated Lévy measure be the m…

The HV1 scheme is an alternating-direction implicit finite-difference scheme for the Heston model, with stability depending on the time-step and spatial discretization through a Co…

Levendorskii's conjecture. The asymptotic formula above holds in this greater generality.