What is Value of a Contract?
Value refers to the notional cost of creating a new contract from simpler items, such as reproducing an option through dynamic buying and selling.
A Short Example
Wheels are $10 apiece. A soapbox costs $20. How much is a go-cart? The value is $60.
A Deep Dive into Value of a Contract
Many people base their understanding of contract value on what they see on a screen or in pricing software. Matters are actually more nuanced than this. Let’s use the above soapbox example.
The go-cart is valued at $60, which includes the soapbox and four wheels, but excludes the cost of nails and labour.
Are you planning to sell the go-cart for $60? I do not believe so. You want to make a profit, so you sell it at $80. That is the price of the go-kart.
Why did someone buy it from you for $80? They must consider $80 as a decent payment. Consider entering a go-carting competition with a $200 first prize. They cannot enter or win the $200 unless they have the go-cart. The chance of winning the prize money makes the go-cart more valuable than $80. They may have gone as high as $100.
This basic example highlights the complexities of the valuation and pricing process. Considering options as go-carts can provide significant insights.
The quant rarely thinks as described above. He considers value and price to be synonymous and uses them interchangeably. And the concept of merit does not appear.
When valuing exotic contracts, quants refer to exchange-traded vanillas to determine the appropriate volatility. This is a calibration. A vanilla exchanges for $10. That’s the price. The quant adjusts the implied volatility of the market from a Black-Scholes valuation method. He assumes that price and value are the same.
Related to this subject is the question of whether a mathematical model explains or characterises a phenomenon. The equations of fluid mechanics, for example, do both.
They are based on the fundamental physics laws of mass and momentum conservation. This contrasts with derivative models.
The Illusion of Calibration
In practice, supply and demand determine prices. In-demand contracts, such as out-of-the-money puts for downside protection, are typically more expensive. This is the reason behind pricing. However, our pricing models do not consider supply or demand.
The models use random walks for the underlying, an unobservable volatility parameter, and assume no arbitrage. Models predict how prices should respond in the presence of volatility. Using our own projection of future volatility in option pricing formulas might result in values that differ from market prices, as evidenced by statistics.
Either our projection is inaccurate and the market has a better understanding, the model is faulty, or both. Common sense suggests that all three are to blame.
Using a valuation technique to remove volatility from supply-demand driven prices is not a valid calibration method.
The quant aims to accomplish similar goals as the go-cart constructor. The go-cart builder does not require a dynamic model for pricing wheels and soapboxes, but instead relies on static calculations. One go-cart is equivalent to one soapbox and four wheels. It is rarely this simple for the quant. His calculations are dynamic, and his hedging adjusts with stock price and time changes. It’s similar like buying more wheels for a go-cart during a race, without knowing the price beforehand. Mathematical models introduce flaws, confusion, and opportunities.
What about worth? That’s a more subjective concept. Quantifying it may necessitate a utilitarian approach. Oscar Wilde once remarked, “A cynic is a man who knows the price of everything but the value of nothing.”
Related Readings
- Put-Call Parity: All You Need To Know
- Modelling Approaches in Quantitative Finance: All You Need To Know
- Central Limit Theorem In Finance: Power Your Portfolio Now