How to Trade with the Black-Scholes Model

Summary

In this video, the speaker discusses how the Black-Scholes model can be applied to trading, specifically in market making and proprietary trading. They emphasize that price prediction is not feasible without insider information, and instead, traders can exploit mispricings using theoretical pricing models. By calculating the fair price of options based on assumptions of asset dynamics, traders can engage in statistical arbitrage to accumulate positive expected value over time. The speaker also acknowledges the limitations of the Black-Scholes model, highlighting the importance of understanding its assumptions and imperfections in achieving long-term profitability.

Takeaways

• 😀 Trading cannot reliably predict the future price of assets without insider information or certainty about upcoming events.
• 😀 The Black-Scholes model is a statistical tool for determining the fair price of options, assuming underlying asset dynamics follow geometric Brownian motion.
• 😀 You don’t need to understand the complex mathematical details of the Black-Scholes formula to use it for trading options.
• 😀 The Black-Scholes model determines the price of an option by considering all potential future states of the world and discounting them back to the present.
• 😀 The market price of options may sometimes be mispriced, which opens the opportunity for statistical arbitrage based on discrepancies from theoretical values.
• 😀 Trading based on Black-Scholes model requires taking advantage of mispricings in the market over many trades, rather than relying on a single trade.
• 😀 The model calculates a theoretical price of an option, but the realized price path and profit or loss (P&L) may differ, as only one path can happen.
• 😀 Consistent profitability is achieved by engaging in a large number of trades that capitalize on mispricing, not by betting on a single event or trade.
• 😀 Casinos and traders alike make money over the long run by surviving short-term losses and maintaining positive expected value over time.
• 😀 While the Black-Scholes model is widely used, it’s imperfect, and assumptions like constant volatility are known to be violated in real markets. Other models, such as stochastic volatility models, can be considered in place of Black-Scholes.

Q & A

What is the Black-Scholes model used for in trading?

The Black-Scholes model is used to determine the fair price of an option, assuming certain dynamics such as geometric Brownian motion for the underlying asset and constant volatility. It helps traders evaluate if an option is mispriced in the market, potentially offering a trading edge.

How does the Black-Scholes model calculate the price of an option?

The model calculates the price of a European call option by taking into account five key inputs: the underlying asset price, the strike price, volatility, the interest rate, and time until maturity. It provides the theoretical fair price based on these factors.

What does the speaker mean by 'there is no such thing as price prediction' in trading?

The speaker emphasizes that predicting the exact future price of an asset is impossible unless you have insider information. Instead, the focus should be on identifying mispricing in the market and capitalizing on statistical arbitrage, rather than attempting to predict price movements.

What role does probability and statistics play in quantitative finance?

Probability and statistics are crucial for quantitative finance because they form the backbone of pricing models like Black-Scholes. These tools help assess the expected return based on different possible outcomes, allowing traders to make informed decisions based on probabilities rather than predictions.

How does statistical arbitrage relate to the Black-Scholes model?

Statistical arbitrage involves exploiting discrepancies between theoretical model prices (like those given by the Black-Scholes model) and the actual market prices. If the model's price is higher than the market price, a trader can buy the option and potentially profit over time as the market corrects the mispricing.

What is meant by a 'positive expected value' in trading?

A positive expected value means that over many trades, the average profit from each trade is expected to be positive. By consistently executing trades based on mispricing identified through models like Black-Scholes, traders can accumulate positive returns over time, even if individual trades may result in losses.

Why is it necessary to trade a large number of contracts to make money with the Black-Scholes model?

The Black-Scholes model provides a statistical edge, but this edge is realized over many trades. A single trade might not yield profit due to market randomness, but as the number of trades increases, the expected value from mispricing will manifest, leading to accumulated profits over time.

What does the speaker mean by 'this is how casinos make money in the long run'?

The speaker compares trading with the Black-Scholes model to how casinos make money. Just as a casino relies on statistical edges and long-term play to accumulate profit, traders can accumulate positive expected value over time by trading based on mispricing, assuming they can survive short-term losses.

What are some limitations of the Black-Scholes model mentioned in the video?

The Black-Scholes model assumes constant volatility and geometric Brownian motion for asset prices, which may not always be accurate in real-world markets. Additionally, it does not account for jumps in price or volatility clustering, which are features observed in actual market behavior.

How can traders deal with the imperfections of the Black-Scholes model?

Traders can acknowledge the model's limitations but still use it effectively by understanding the assumptions behind it and being aware of environments where these assumptions might hold true or be violated. Other models, such as those incorporating stochastic volatility or jump diffusion, can be used for different market conditions.