arXiv subjects

Shuxin Guo

Publications and source records attributed to Shuxin Guo.

4 recordsLinked to original sources

arXiv2024

Risk-neutral valuation of options under arithmetic Brownian motions

On April 22, 2020, the CME Group switched to Bachelier pricing for a group of oil futures options. The Bachelier model, or more generally the arithmetic Brownian motion (ABM), is not so widely used in finance, though. This paper provides the first comprehensive survey of options pricing under ABM. Using the risk-neutral valuation, we derive formulas for European options for three underlying types, namely an underlying that does not pay dividends, an underlying that pays a continuous dividend yield, and futures. Further, we derive Black-Scholes-Merton-like partial differential equations, which can in principle be utilized to price American options numerically via finite difference.

q-fin.PR↗

arXiv2024

The Black-Scholes-Merton dual equation

We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European, American, Bermudan, Asian, barrier, lookback, etc., and leads to new insights into pricing and hedging. Perceptibly, a put-call equality emerges - all the put options can be priced as their corresponding calls by simultaneously swapping stock price (dividend yield) for strike price (risk-free rate), and vice versa. Equally important, we provide simple analytic formulas for hedging parameters delta and gamma, which elevate the put-call equality to true practical applicability. For futures options, the put-call equality leads to "symmetric" properties between puts and calls or among puts (calls).

q-fin.PR↗

arXiv2024

Is the annualized compounded return of Medallion over 35%?

It is a challenge to estimate fund performance by compounded returns. Arguably, it is incorrect to use yearly returns directly for compounding, with reported annualized return of above 60% for Medallion for the 31 years up to 2018. We propose an estimation based on fund sizes and trading profits and obtain a compounded return of 31.8% before fees. Alternatively, we suggest using the manager's wealth as a proxy and arriving at a compounded growth rate of 25.6% for Simons for the 33 years up to 2020. We conclude that the annualized compounded return of Medallion before fees is probably under 35%. Our findings have implications for correctly estimating fund performance.

q-fin.PM↗

arXiv2024

Data-generating process and time-series asset pricing

We study the data-generating processes for factors expressed in return differences, which the literature on time-series asset pricing seems to have overlooked. For the factors' data-generating processes or long-short zero-cost portfolios, a meaningful definition of returns is impossible; further, the compounded market factor (MF) significantly underestimates the return difference between the market and the risk-free rate compounded separately. Surprisingly, if MF were treated coercively as periodic-rebalancing long-short (i.e., the same as size and value), Fama-French three-factor (FF3) would be economically unattractive for lacking compounding and irrelevant for suffering from the small "size of an effect." Otherwise, FF3 might be misspecified if MF were buy-and-hold long-short. Finally, we show that OLS with net returns for single-index models leads to inflated alphas, exaggerated t-values, and overestimated Sharpe ratios (SR); worse, net returns may lead to pathological alphas and SRs. We propose defining factors (and SRs) with non-difference compound returns.

q-fin.GN↗