arXiv subjects

Nicola Cantarutti

Publications and source records attributed to Nicola Cantarutti.

3 recordsLinked to original sources

arXiv2023

Silkswap: An asymmetric automated market maker model for stablecoins

Silkswap is an automated market maker model designed for efficient stablecoin trading with minimal price impact. The original purpose of Silkswap is to facilitate the trading of fiat-pegged stablecoins with the stablecoin Silk, but it can be applied to any pair of stablecoins. The Silkswap invariant is a hybrid function that generates an asymmetric price impact curve. We present the derivation of the Silkswap model and its mathematical properties. We also compare different numerical methods used to solve the invariant equation. Finally, we compare our model with the well-known Curve Finance model.

q-fin.CP↗

arXiv2019

Option pricing in exponential Lévy models with transaction costs

We present an approach for pricing European call options in presence of proportional transaction costs, when the stock price follows a general exponential Lévy process. The model is a generalization of the celebrated work of Davis, Panas and Zariphopoulou (1993), where the value of the option is defined as the utility indifference price. This approach requires the solution of two stochastic singular control problems in finite horizon, satisfying the same Hamilton-Jacobi-Bellman equation, with different terminal conditions. We introduce a general formulation for these portfolio selection problems, and then we focus on the special case in which the probability of default is ignored. We solve numerically the optimization problems using the Markov chain approximation method and show results for diffusion, Merton and Variance Gamma processes. Option prices are computed for both the writer and the buyer.

q-fin.MF↗

arXiv2018

Multinomial method for option pricing under Variance Gamma

This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same firsts four cumulants. This approach is particularly convenient for pricing American and Bermudan options, which can be exercised at any time up to expiration date. Numerical computations of European and American options are presented, and compared with results obtained with finite differences methods and with the Black Scholes model.

q-fin.PR↗