Skip to content

Delta of a one-year at-the-money call at 6% rates

Question

A one-year European call is struck at the current stock price; the rate is 6%6\% and the stock pays no dividends. Is its delta larger or smaller than 0.50.5, and what determines this?

Short answer

Larger than 0.50.5. At the money d1=(r+12σ2)TσT>0d_1 = \frac{(r + \frac12\sigma^2)T}{\sigma\sqrt T} > 0, so Δ=N(d1)>0.5\Delta = N(d_1) > 0.5. Both the positive rate (the forward sits above the strike) and the 12σ2\tfrac12\sigma^2 term from lognormal skew push it up.

Adapted from Crack, Heard on the Street, Q2.5, p.24; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free