WOLFRAM|DEMONSTRATIONS PROJECT

Options Board Using Black-Scholes Prices

​
stock volatility (%)
30.
risk-free rate (%)
5.
days to next expiry
12
spot price
100.
Calls
Puts
bid
ask
strike
bid
ask
11 SEP 2023
5.60
5.65
95.00
0.45
0.50
3.70
3.75
97.50
1.05
1.10
2.25
2.30
100.00
2.05
2.10
1.20
1.25
102.50
3.55
3.60
0.55
0.60
105.00
5.40
5.45
11 OCT 2023
7.30
7.35
95.00
1.75
1.80
5.70
5.75
97.50
2.65
2.70
4.30
4.35
100.00
3.75
3.80
3.20
3.25
102.50
5.10
5.15
2.30
2.35
105.00
6.70
6.75
10 NOV 2023
8.65
8.70
95.00
2.70
2.75
7.10
7.15
97.50
3.65
3.70
5.75
5.80
100.00
4.80
4.85
4.60
4.65
102.50
6.10
6.15
3.65
3.70
105.00
7.60
7.65
In this Demonstration, we show a simple options board for a hypothetical stock. The board shows bid and ask prices for calls and puts for several monthly expiration dates and a range of strike prices that are close to the money. The prices are calculated using the Black–Scholes model and the bid-ask spread are five cents wide (and are about the actual Black–Scholes price). By changing the model parameters (volatility, interest rate, and time to expiry), together with the underlying stock price, it is possible to get a feel for how option prices of different strike and expiry are affected.