Stochastic Volatility Models and its Effect on the Asset Market

Nandkishor J, Applied Sciences, 22F

This paper delves into the significance of Stochastic Volatility (SV), a fundamental economic concept used in determining patterns and fluctuations in asset market prices. Stochastic refers to a random probability distribution or pattern that can be statistically analyzed but cannot be precisely predicted. Attempting to find a pattern in randomness and attempting to predict it is fascinating. Volatility is the tendency for prices to fluctuate rapidly and unexpectedly.

SV refers to the fact that asset price volatility varies. Even financial models, such as the Black-Scholes model, rely on time-varying volatility to calculate the prices (Hayes, 2022b). Black-Scholes model is a differential equation used to price options contracts. A stock option (also known as an equity option), gives an investor the right, but not the obligation, to buy or sell a stock at an agreed-upon price and date (Chen, 2022). An option contract is an agreement that enforces this.

The SV models are equations that were crafted to be used in multiple fields. It was invented to solve a drawback of the Black-Scholes model (the model mentioned earlier). The Black-Scholes model was created in 1973 by three incredible scientists: Fischer Black, Robert Merton, and Myron Scholes. It is a pricing model based on six variables; volatility, type of option, underlying stock price, time, strike price and risk-free rate.

It has simplified things to the point where we only need to enter six figures into a financial calculator to see the future predicted rates for any stock option or other type of asset. This model now assumes that volatility remains constant over the life of the option (the period of owning the stock option), which is not the case because volatility varies with supply and demand. And this is where SV comes in. The Black-Scholes model assumed that the volatility is constant over the life of the derivative (financial contract whose value depends on assets), and unaffected by the varying price levels. This assumption led to inaccurate future predictions in some cases. SV model attempts to correct this by taking into consideration the volatility that fluctuates over time, leading to a more precise calculation (Hayes, 2022a).

The most important application of this concept is in the stock markets, and it was created with the stock markets in mind. Many stochastic volatility models were developed in the early 1970s. We can get a rough idea of future projections thanks to these models, and we can visualize them using charts and other mathematical tools.

Investors must now decide which stocks to invest in. High volatility indicates a greater deflection either upwards or downwards, implying that risks are high. However, the rewards are also high. People who do not want to play risky can invest in low volatile shares which have a steady rate of growth and may enjoy something like (for example) 1% monthly growth and 13% annual growth. The world of statistics is full of fascinating theories and concepts that are fascinating to learn. Having more knowledge brings more money. One must be financially savvy to make the most of their money.

References

Chen, J. (2022, August 30). What Are Stock Options? Parameters and Trading, With Examples. Investopedia. https://www.investopedia.com/terms/s/stockoption.asp

Hayes, A. (2022a, June 3). Black-Scholes Model: What It Is, How It Works, Options Formula. Investopedia. https://www.investopedia.com/terms/b/blackscholes.asp

Hayes, A. (2022b, August 28). Stochastic Velocity. Investopedia. https://www.investopedia.com/terms/s/stochastic-volatility.asp