Introduction and Calculation of BTC & ETH Options

Pricing Volatility

This topic introduces options contracts based on Bitcoin (BTC) and Ethereum (ETH), exploring their characteristics and basic valuation concepts.

A. What are BTC & ETH Options?

• Definition: Options contracts that give the buyer the right, but not the obligation, to buy (call option) or sell (put option) Bitcoin or Ethereum at a specified price (strike price) on or before a specified date (expiration date).
• Key Concepts (Review):
  • Call Option: The right to buy the underlying asset.
  • Put Option: The right to sell the underlying asset.
  • Strike Price (K): The price at which the underlying asset can be bought or sold if the option is exercised.
  • Expiration Date (T): The date on which the option expires.
  • Premium: The price paid by the option buyer to the option seller.
  • European Style: Can only be exercised at expiration.
  • American Style: Can be exercised at any time before expiration.
• Where to Trade:
  • Centralized Exchanges: Deribit, OKEx, CME (for BTC).
  • Decentralized Exchanges (DEXs): Opyn, Hegic (though liquidity can be limited).
  • CME only provides BTC, so you would need to look to Deribit to get these formulas for ETH as well.
• Settlement: Typically cash-settled in USD or stablecoins (like USDT or USDC).

B. Factors Affecting BTC & ETH Option Prices:

The price of a BTC or ETH option is influenced by several factors, similar to traditional options:

1. Price of the Underlying Asset (S):
   • Call options increase in value as the price of BTC/ETH increases.
   • Put options increase in value as the price of BTC/ETH decreases.
2. Strike Price (K):
   • The relationship between the strike price and the underlying asset price determines whether the option is in the money, at the money, or out of the money.
3. Time to Expiration (T):
   • The longer the time to expiration, the more valuable the option (all else being equal) because there is more time for the underlying asset price to move in a favorable direction.
4. Volatility (σ):
   • Higher volatility increases the value of both call and put options because there is a greater chance of a large price move.
   • Implied Volatility (IV) is a key metric for crypto options.
5. Risk-Free Interest Rate (r):
   • Has a smaller impact on short-term options, but higher interest rates generally increase call option prices and decrease put option prices. This factor is often less significant for crypto options compared to traditional options. C. Basic Option Payoff Formulas:

• Call Option Payoff (at Expiration):

  • Max(0, S - K)

• Put Option Payoff (at Expiration):

  • Max(0, K - S)

D. Valuation Models (Introduction):

• Black-Scholes Model: The Black-Scholes model (or variations thereof) is sometimes used to value BTC and ETH options, but it has limitations because it assumes:
  • Constant Volatility: Crypto volatility is notoriously not constant.
  • Efficient Markets: Crypto markets can be inefficient.
  • Continuous Trading: Crypto trading is often 24/7, which can violate the assumptions of the model.
• Garman-Klass Volatility: Some traders use the Garman-Klass volatility estimator, which takes into account the open, close, high, and low prices of an asset, to better estimate the volatility of crypto assets.
• Binomial Tree Model: A more flexible model that can be used to value American-style options and can accommodate time-varying volatility.
• Monte Carlo Simulation: Can be used to value complex options with path-dependent payoffs.
• Market Prices: Ultimately, the most important factor in determining the price of a BTC or ETH option is the market price. Supply and demand, sentiment, and other market forces play a significant role.

E. Considerations Specific to Crypto Options:

• 24/7 Trading: Crypto markets trade 24/7, which can affect option pricing and hedging strategies.
• High Volatility: Crypto assets are known for their high volatility, which can lead to large swings in option prices.
• Regulatory Uncertainty: The regulatory landscape for crypto options is still evolving, which can create uncertainty.
• Custody and Security: Ensuring the safe custody and security of the underlying BTC or ETH is crucial.
• Funding Rates: High, regular funding rates paid on many crypto assets can influence the Black-Scholes Model.

F. Example (Simplified):

Let's say Bitcoin is trading at $30,000. You buy a call option with a strike price of $32,000 and an expiration date in one month. The premium is $1,000.

• If, at expiration, Bitcoin is trading above $32,000, you will exercise the option and make a profit (minus the premium).
• If, at expiration, Bitcoin is trading at or below $32,000, you will not exercise the option, and your loss is limited to the $1,000 premium.