100 - Introduction

# The true price of an option

What is the true price of an option? ORATS has spent the last 20 years fine tuning calculations and methodologies to answer this question.

## The standard model

To understand our approach, let’s first look at the five components of a standard options pricing model.

- Strike price
- Time to expiration
- Underlying stock price
- Interest and dividend rates
- Implied volatility

Out of these five components, implied volatility is the most important.

### Implied volatility

Implied volatility is the least known, but also the most impactful component of the option price. In a perfect world, all of the options at all strikes and expirations for an underlying would have the same implied volatility, even though the options prices are different. This is the “constant volatility” that Black and Scholes assumed to be true in their original equation. However, in the real world, implied volatility is different for almost every strike and expiration.

You might be wondering, doesn’t the option chain already tell me the volatility? Well, you’re not wrong. Most standard options chains include the call and put implied volatility, calculated using the mid price or the last traded price as the “plug”. So instead of solving for price, you make implied volatility the unknown value, and solve for it using the market price.

However, this is a rather crude way of calculating implied volatility. There are some common pitfalls when using this approach.

### Pitfalls

- You usually end up with different call and put implied volatilities for the same strike.
- As you drift further away from the at-the-money strike, the smaller delta calls and puts have lower premium, and the implied volatility becomes less realistic.
- Illiquid securities or options with a wide bid-ask spread can have unreliable mid or last prices, causing the implied volatility to be off.

Why are these pitfalls important? They might seem unimportant right now, but they make a big difference in the long run. Have you ever heard of the adage, “The flapping of the wings of a butterfly can be felt on the other side of the world”? Because implied volatility is the primary component of option pricing, an incorrect calculation can lead to poor quality backtests, inaccurate Greeks, and inefficient risk management, culminating in a negative effect on your bottom line.

## The ORATS solution

Enter the ORATS Smoothed Market Values (SMV) process - a meticulously crafted series of equations that calculates accurate implied volatilities for each option, laying the foundation for accurate backtesting, scanning, execution, and risk management. Instead of simply deriving volatility from the market price, we look at several other contributing factors.

### Interest rate assumptions

Interest rate assumptions can vary over stocks, expirations and even strikes. Stocks can be hard-to-borrow and instead of receiving interest for being short shares, interest is paid for the privilege of shorting these stocks. Since the hard-to-borrow-ness of a stock can change and usually fade over time, farther out expirations will have a lower hard to borrow rate than near months.

### Dividend assumptions

We source our dividend information from Wall Street Horizon, a popular and reliable source of dividend information. We also employ an in-house dividend consultant for special cases and quality control. Whether or not there is a dividend paid during the options lifecycle will impact the volatility and price.

### Liquidity

Market makers will often have wider spreads on a high absolute delta option than the low one. For example, an in-the-money, low strike, high delta call, will likely have a wider spread than its partner put. Market makers will have to hedge the buying or selling of this call and that hedge usually involves buying or selling the underlying. The call will have more deltas to hedge and more risk to the market maker and this will often cause a wide bid-ask spread. Moreover, the market maker may determine that selling the deltas are harder than buying deltas.

## Technical details

In options trading, calls and puts should have the same implied volatility, which describes the portion of the options price attributable to the movement in the stock. Imbalances in implied volatility are caused by the factors above. ORATS works to isolate these factors and solve for the residual yield that lines up call and put implied volatilities. By doing so, call and put implied volatilities can be made equal.

### Drawing a smooth curve

With the call and put implied volatilities lined up, we have a single measurement of implied volatility for every strike. This allows us to fit a non-arbitrageable smooth curve through these values. To make it non-arbitrageable, we…

- Use a proprietary skew generator using bounded flexible spline bands.
- Adjust the skews with another process to account for wings that may be slightly off put-call parity.
- liminate calendar or butterfly arbitrage in our theoretical values.

If this is too technical, don’t worry. All you need to know is that we’ve now built a single, smooth curve that accurately represents implied volatility across all strikes and expirations, opening us up to a world of better options analysis. The pitfalls described earlier have been avoided, and we can finally answer the question, “What is the true value of an option”?

### Implementation

Using the SMV implied volatility value for each option, we can plug it into the pricing model defined at the beginning of the lesson, and solve for a theoretical options price. This price can can then be compared to market bid-ask quotes to see if the options are under or overpriced.

While this is a great achievement, the SMV process we just discussed has many more applications. In the coming lessons, we will discuss why this is just the tip of the iceberg, and how the SMV process creates hundreds of new indicators that you can use to make smarter trading decisions.