# OKEx Crypto Options Principles and Strategies I: Put-Call Parity

Dec 27, 2019 · 3 min read

We have announced the introduction of BTC options, which is expected to roll out to the public in January 2020. Following the launch of early access to select clients on Dec 26, we have also prepared this series of articles for our users to familiarize themselves with the crypto options’ principle and strategies, pointing out differences from conventional market or theory.

# I.Put-Call Parity

As indicated on our Factsheet and industry-wise, Black-Scholes(BS) model has been used as a standard (at least starting point) for European pricing options. Even though there is criticism on its model assumptions and known limitations, compared to real market behavior and data, its closed form and less efforts on simulation bring still a de facto model in the options world.

Compared to the BS model, especially which requires dynamic hedging, Put-Call Parity has been recognized as static replication(hedging), which entails less transaction, theoretically.

Put-Call Parity

where:

• C is the value of the call option
• P is the value of the put option, with the same expiration and strike of call
• S is the spot price
• K is the strike(exercise) price
• D is the discounting factor with respect to risk-free rate and time to expiration

As shown above, the difference between call and put option price is equivalent to the difference of current spot and strike price, discounted to present values. If this equilibrium breaks, there exists an arbitrage opportunity, theoretically.

# II.How this principle can be used as a trading strategy?

By plugging the current market values, we can check the equation is working. Using a simple algebraic rule, Put-Call parity can be rewritten in this formula.

For example, assuming that the current spot price of BTC is traded at 8,000, and discounted strike price with respect to time and the risk-free rate is 7,850. And, found in the market that call option price is 1,160 and Put is 1,010 for same strike, same expiry option. Thus, 8,000–1,160 + 1,010–7,850 = 0, shows put-call parity is working. AND if those not equal to zero, then there is a chance for trading. However, please be aware that those option prices are based on BTC, so will be on the market as 0.1450 (:= 1,160/8,000), 0.1263 (:= 1,010/8,000), respectively.

Furthermore, even OKEx BTC option is not designed as an option on futures, however, as futures price is based on the same index, same time horizon to daily settlement, maturity, market’s risk-free rate, etc, it’s worthwhile to cross-check our futures and perpetual swap market as proxy and possible opportunity. As market matures, those relationship will be strengthened. In that case, the alternative Put-Call Parity formula, which may help your easier calculation, is given below.

where:

• F is the value of the futures contract with the same expiry, and others remain same

So, you can see the difference that discounting factor is derived since spot price is the present value of futures price, discounted with respect to time and risk-free rate.

At the start of simulation trading period, we have seen pretty odd, jumpy, unstable prices and volatilities. However, at the end of the term, we observed better shape of volatility surfaces and price connection to the existing markets. At the time of live trading, we are expected to see this, but will find the right and healthy figure soon. Thus, as indicated via this article and targeting ourselves as one-stop cryptocurrency exchange, OKEx BTC option would contribute the price discovery and transparency, well-managed volatility of whole crypto markets, leading to the integrated global financial system.

Disclaimer: This material should not be taken as the basis for making investment decisions, nor be construed as a recommendation to engage in investment transactions. Trading digital assets involves significant risk and can result in the loss of your invested capital. You should ensure that you fully understand the risk involved and take into consideration your level of experience, investment objectives and seek independent financial advice if necessary.

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