Question

Calculate the beta of the January 2010 $9 call option (maturing on January 15, 2010) on JetBlue listed in the Table Assume that the volatility of JetBlue is 64.7% per year and its beta is 0.86. The short-term risk-free rate of interest is 2.31% per year. What is the option's leverage ratio? Use a 365-day year. (Note: Make sure to keep all variables and intermediate steps rounded to at least six decimal places.) TABLE 21.1 JetBlue Option Quotes JBLU 5.03 +0.11 Vol 7335887 Jul 24 2009 @ 17:17 ET Bid 5.03 Ask 5.04 Size 168 96 Open Open Calls Bid Ask Vol Puts Bid Ask Vol Int Int 09 Dec 5.00 (JGQ LA) 09 Dec 5.00 (JGQ XA) 0.80 0.90 47 5865 0.80 0.90 6 1000 09 Dec 6.00 (JGQ LF) 0.45 09 Dec 6.00 (JGQ XF) 1.40 2 0 0.55 259 1.50 84 10 Jan 5.00 (JGQ AA 0.85 1.00 125 10 Jan 5.00 (JGQ MA 0.85 6433 0.95 10 14737 10 Jan 6.00 JGQ AF) 0.50 10 Jan 6.00 (JGQ MF) 1.45 22 0.60 28 1.55 10 Jan 9.00 (JGQ A) 0.05 0.15 818 10 Jan 9.00 (JGQ MI) 4.00 0 0 4.10 10 Mar 5.00 (JGQ CA 10 Mar 5.00 (JGQ OA) 1.05 1.15 50 1.00 1.10 0 40 10 Mar 6.00 (JGQ OF 10 Mar 6.00 (JGQ CF) 0.65 0 146 1.60 1.70 0.75 10 41 0.50 10 Mar 7.00 (JGQ CG) 10 Mar 700 (JGQ OG) 0.40 3 2.30 2.45 10 0 Source: Chicago Board Options Exchange at www.cboe.com

Answer 1

Here number of days = 188 days

strike X  = 9

spot S = 5.03

Risk-free rate = 2.31

δ=N(d1)

In(r ovt N (d1)where d1

After calculation,  

we found delta of the call to be $\Delta$ = 0.159 of call

Beta of stock $\beta$= 0.86

Beta of call = (S/X) *Δ *β = ( 5.03 /9)*0.159*0.86 = 0.075

K	Option strike price
N	A standard normal cumulative distribution function
r	Risk-free interest rate
σ	The volatility of the underlying
S	Price of the underlying
t	Time to option's expiry

Options leverage ratio : ( delta of call * stock price - option price ) / option price , option price = 0.15 ; so

Options leverage is 4.332