【专题研究】期权：量化视角评估期权组合效益（一）

Quantitative Models and Construction Methods 1. Model Name: Monte Carlo Simulation for Methanol Futures Pricing - Model Construction Idea: The model assumes that under risk-neutral conditions, the price movement of futures follows a stochastic process. This allows for the simulation of future price paths to evaluate the profitability of the "short strangle" options strategy[7][8]. - Model Construction Process: 1. Assume the futures price follows the stochastic differential equation: $\frac{dS_t}{S_t} = \mu dt + \sigma dB_t$ where $S_t$ is the futures price at time $t$, $\mu$ is the risk-free rate, $\sigma$ is the volatility, and $dB_t = \epsilon \sqrt{dt}$ ($\epsilon$ follows a standard normal distribution)[7]. 2. Using Ito's Lemma, transform the equation into: $d(\ln S) = \left(\mu - \frac{\sigma^2}{2}\right)dt + \sigma dB$[8] 3. Derive the relationship between the futures prices at two time points: $S_T = S_t \cdot \exp\left[\left(\mu - \frac{\sigma^2}{2}\right)(T-t) + \sigma \epsilon \sqrt{T-t}\right]$[9] 4. Simulate the price paths using Monte Carlo methods: - Divide the time horizon into small intervals (e.g., one trading day). - Generate 1,000 random paths for the futures price using the above formula. - Store the simulated prices in an $M \times N$ matrix, where $M$ is the number of paths and $N$ is the number of time intervals[10]. - Model Evaluation: The Monte Carlo simulation effectively captures the stochastic nature of futures price movements and provides a robust framework for evaluating options strategies under different scenarios[10]. --- Model Backtesting Results 1. Monte Carlo Simulation Model - Annualized Return Matrix (Prediction): The highest predicted annualized return is 23.00% for the C2600-P2550 combination[13]. - Win Rate Matrix (Prediction): The highest predicted win rate is 100.00% for multiple combinations, including C2950-P2075 and C3050-P2075[14]. - Win Rate * Return Matrix (Prediction): The highest combined value is 16.30% for the C2600-P2550 combination[16]. --- Quantitative Factors and Construction Methods 1. Factor Name: Short Strangle Options Strategy (C2600-P2550 Combination) - Factor Construction Idea: The short strangle strategy involves selling a low-strike put option and a high-strike call option. This strategy is suitable for scenarios where the underlying asset's price is expected to exhibit low volatility[3]. - Factor Construction Process: 1. Select a low-strike put option (e.g., P2550) and a high-strike call option (e.g., C2600). 2. Sell both options to collect premiums. 3. The profit/loss structure is determined by the difference between the collected premiums and the payoff at expiration, depending on the underlying asset's price[3]. - Factor Evaluation: The strategy is well-suited for assets with low expected volatility, as it benefits from limited price movement. In this case, the methanol futures market's low historical volatility and low seasonal open interest support the strategy's feasibility[5][6]. --- Factor Backtesting Results 1. Short Strangle Options Strategy (C2600-P2550 Combination) - Annualized Return: 23.00%[13]. - Win Rate: 66.70%[14]. - Win Rate * Return: 16.30%[16].