The Black Scholes model, or Black Scholes formula, is the world’s most well-known pricing model for options.
The Black Scholes pricing model is important because anyone can use it to assess the value of an option. This article will explain the basics of the Black Scholes model and why it is important to understand.
This model was developed in 1973 and stands as one of the most important concepts in modern financial theory. The Black Scholes formula gives a theoretical estimate for the pricing of European call and put options.
Investors can go online to websites such as this one to use the Black Scholes calculator. Have no fear, since understanding the underlying math behind the formula is not necessary for its use.
Some things to note about the Black Scholes formula are: it is only used for options that do not pay dividends, and it is for European-style options. European options differ from American options because European options only can be exercised on the expiration date, whereas American options can be exercised before, or on, the expiration date.
The Black Scholes formula contains the underlying stock price, the strike price, the time until maturity, the risk-free interest rate and the volatility of the stock price. These things must be inputted into the Black Scholes calculator to use it.
The formula and the explanation of the formula (see below) is taken from this article.
- C0 = S0 N(d1) – Ke-rT N(d2) Where, C0 = the price of a European-style call option that does not pay dividends S0 = the price of the underlying stock at the time of valuation d1 = (ln(S0/K) + (r + σ2/2)T)/(σ√T) N(d1) = a statistical measure (normal distribution) corresponding to the call option’s delta d2 = d1 – (σ√T) N(d2) = a statistical measure (normal distribution) corresponding to the probability that the call option will be exercised at expiration Ke-rT = the present value of the strike price r = the risk-free interest rate T = the time remaining to expiry, in years σ = the volatility of the price of the underlying stock
Here is an example of this formula in action.
- Consider a European call option on the stock of Shopify Inc. (NYSE: SHOP). This security does not pay dividends and is trading at $114.92 on June 16, 2017. We will choose a strike price of $110 with an expiration on January 19, 2018.
S0 = $114.92, K = $110, r = 0.57%, σ = 43.82%, T = 0.59 (217 days) We are looking for: C0 = S0 N(d1) – Ke-rT N(d2) The following results are obtained: Ke-rT = $109.63 d1 = 0.3083 d2 = -0.0283 N(d1) = 0.6211 N(d2) = 0.4887 C0 = $114.92 x 0.6211 – $109.63 x 0.4887 C0 = $71.37 – $53.58 C0 = $17.80
This is a good example of the Black Scholes formula in action used to find the value of the SHOP option: $17.80.
Understanding this formula isn’t necessary to be a successful options trader. However, understanding how to use the Black Scholes calculator online is an important tool to have. It allows an investor to calculate on his own the value of the options they may want to trade.