We are considering a stock option with following information:

1. Option type: calls
2. Expiry date: 22/05/2020
3. Strike price: $1250
4. Option price: bid:$71.80, ask:76.10
5. Historical Volatility(30 days):0.516

S₀: Stock Spot price today

S_k: Strike price

T: Time until delivery date

r: Risk-free interest rate

: volatility of stock price

Assuming we enter the option on 23 April 2020,

S₀ = $1,276.31 (Stock spot price @ 23 April, 2020)

T = 1 months

r = 0.16% per annum = 0.1599% with continuous compounding (1 year Treasury Bill Rate)

Model Price Calculation

We will calculate the u, d, p for a two step tree,

In our case, t=0.5/12,

Up step size u=e^50%*0.5/12=1.0211

Down step size d=1/u=0.9794

Probability of up move p=(e^{0.1599%*0.5/12}-0.9794)/(1.0211-0.9794)=0.4956, 1-p=0.5044

After using two step trees

We get the Option value

f=[(0.4956²*80.73)+(2*0.4956*0.5044*26.39)+(0.5044²*0)]*e^{(-0.1599%*1/12)}

Option value f=33.018

What relationship is the market price and the calculated option value?