Which relationship holds with the most precision?

Question

BlackTom AI · Accepted Answer

We start by listing the options to compare what relationship or concept each one describes.
Option 1: 'C = F(S,K,r,t,σ) where F = Black-Scholes model, σ = 100-day historical volatility and C = observed call price'. This suggests a pricing formula that ties call price to Black-Scholes with a specific σ. In reality, Black-Scholes uses a forward-looking, implied volatility, risk-free rate, and continuous time dynamics; using a fixed 100-day historical σ and equating C directly to an observed price is not a precise, universal relationship. It mixes historical and model-based components in a way that does not guarantee exact equality in all market conditions, making it less precise.
Option 2: 'Expectations Hypothesis'. The Expectations Hypothesis concerns the term structure of interest rates and expectations about future rates. It is a distinct concept from option pricing relationships and does not provide a precise arbitrage-based equality for option prices, so it is not the most precise relationship in this context.
Option 3: 'Put-Call Parity'. Put-Call Parity is a fundamental arbitrage relationship that links European call and put prices with the underlying asset price and the strike price discounted by the risk-free rate. It has a precise, universal formula (C - P = S0 − K e^{-rt}) and holds under no-arbitrage conditions, making it the most exact relationship among the options listed.
Option 4: 'Credit spread on a corporate bond = output of the Merton Model'. The Merton Model connects a firm's asset value to credit spreads in a structural credit framework, but stating that the credit spread is the direct output of the model is not as general or precise as a parity relationship. It describes a modeling framework rather than a single exact price relationship for options.

In summary, option 3 points to a definitive and exact financial relationship (Put-Call Parity) that holds under standard assumptions, whereas the other options describe models or hypotheses that are either less precise or contextually different, which makes them weaker as a universal relationship.

IFEPIA7022_001_2025_3 - Economics of Finance EOF Final - Dec 16, 2025

Which relationship holds with the most precision?

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