“Binary options are options with discontinuous payoffs. A simple example of a binary option is a cash-or-nothing call. This pays off nothing if the asset price ends up below the strike price at time T and pays a fixed amount, Q, if it ends up above the strike price. In a risk-neutral world, the probability of the asset price being above the strike price at the maturity of an option is, with our usual notation, N(d2). The value of a cash-or-nothing call is therefore Qe-rTN(d2). A cash-or-nothing put is defined analogously to a cash-or-nothing call. It pays off Q if the asset price is below the strike price and nothing if it is above the strike price. The value of a cash-or-nothing put is Qe-rTN(-d2).”
Using Excel (or otherwise), calculate the price of a binary call option on your stock maturing on
January 19, 2018 that pays $100 if the stock price ends up below the strike that is closest to being at-the-money and zero otherwise (give your answer in dollars, to 4 d.p.).