# Non-traded call's volatility smiles

## TL;DR

This paper investigates the formation of volatility smiles in options pricing by considering real-world hedging imperfections and the impact of stock drift exceeding the risk-free rate, framing prices as fair game expectations.

## Contribution

It introduces a fair game approach to option pricing that accounts for hedging imperfections and drift effects, explaining the origin of volatility smiles.

## Key findings

- Volatility smiles arise from hedging imperfections.
- Higher stock drift relative to risk-free rate influences option prices.
- Prices can be viewed as fair game expectations based on payoffs and risk.

## Abstract

Real life hedging in the Black-Scholes model must be imperfect and if the stock's drift is higher than the risk free rate, leads to a profit on average. Hence the option price is examined as a fair game agreement between the parties, based on expected payoffs and a simple measure of risk. The resulting prices result in the volatility smile.