Explain the relationship between implied volatility and option pricing, and discuss the limitations of using implied volatility as a measure of market risk.

Implied volatility is a crucial factor in option pricing. It represents the market's expectation of future price volatility for the underlying asset. Essentially, it's the volatility that, when plugged into an option pricing model like the Black-Scholes model, produces the observed market price of the option.

Here's how it works:

1. Option Pricing Models: Option pricing models, such as Black-Scholes, require inputs like the underlying asset's price, strike price, time to maturity, risk-free rate, and volatility.
2. Implied Volatility: The market price of an option is readily available. By feeding the other known inputs into the model and adjusting the volatility until the model's output matches the market price, we arrive at the implied volatility.
3. Relationship: Higher implied volatility indicates a higher expectation of price fluctuations in the underlying asset. This translates to higher option prices, as options become more valuable when there's a greater chance of large price swings.

For example, if the market is expecting a volatile period for a particular stock, the implied volatility for its options will be higher. This will lead to higher option premiums, as traders are willing to pay more for the right to buy or sell the stock at a predetermined price in a volatile market.

However, using implied volatility as a measure of market risk has limitations:

1. Backward-Looking: Implied volatility is derived from current option prices, making it a backward-looking measure. It doesn't necessarily reflect future volatility accurately.
2. Not a True Measure of Risk: Implied volatility doesn't capture all aspects of market risk. It focuses solely on price fluctuations, neglecting other risks like liquidity risk, counterparty risk, and model risk.
3. Affected by Market Sentiment: Implied volatility can be inflated by market sentiment. For instance, during periods of high fear and uncertainty, options prices tend to be inflated, resulting in higher implied volatility, even if actual price movements remain moderate.
4. Not Always Reliable: Implied volatility can be influenced by factors like the option's strike price and time to maturity, making it difficult to compare implied volatilities across different options or assets.

Therefore, while implied volatility is a useful tool in understanding market expectations of price volatility, it's crucial to be aware of its limitations and use it with caution when assessing market risk. Combining implied volatility with other risk measures and considering market context is essential for a more comprehensive risk assessment.