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Fundamental Theorem of Discrete Asset Pricing
Masaaki Fukasawa
Motivated by discrete price quotes in continuous time, we seek a fundamental theorem based on no arbitrage rather than a condition on limiting trading opportunities. We consider a…
Loss-versus-rebalancing with external proportional transaction costs
Masaaki Fukasawa
We study liquidity provision in automated market makers when trading in the external market incurs proportional transaction costs. We consider both separately collected fees and fe…
Short-term barrier option price expansion
Masaaki Fukasawa
We derive a short-maturity expansion for up-and-out put barrier option prices under continuous stochastic volatility when the strike and the barrier approach the spot at the diffus…
Basket implied volatility skew and stickiness
Masaaki Fukasawa, Jun Maeda, Tatsuya Ogiwara
We study the short-maturity implied volatility and the skew stickiness ratio for baskets of assets with continuous, possibly rough, stochastic volatility. The fluctuation of the in…
Yet another asymptotic formula for implied volatility
Masaaki Fukasawa
We derive a first-order representation of Black-Scholes implied variance in a continuous local martingale model. Total implied variance is the conditional expectation of the quadra…
Short-maturity skew stickiness ratio under local volatility
Masaaki Fukasawa
We prove that the skew stickiness ratio converges to two at short maturity under local volatility models. This appears to be the first rigorous proof of this limit for a general ti…
Error Distribution of the Local Linearization Method for Stochastic Differential Equations with Additive Brownian Noise
Masaaki Fukasawa, Mikio Hirokane, Kostas Kardaras
We prove a functional stable limit theorem for the discretization error process of a local linearization scheme for stochastic differential equations with additive Brownian noise.…
Martingale expansion for stochastic volatility
Masaaki Fukasawa
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theor…
On the Skew Stickiness Ratio
Masaaki Fukasawa
The skew stickiness ratio is a statistic that captures the joint dynamics of an asset price and its volatility. We derive a representation formula for this quantity using the Itô-W…