On November 21, 2007, Citigroup (C) stock was trading around $30 a share. Its Ja

Question

On November 21, 2007, Citigroup (C) stock was trading around $30 a share. Its January call with exercise price of $27.5 traded for $4. The risk-free rate was 4%. Compute the theoretical option values at standard deviations of returns at (a) 20% (b) 40% (c) 60%. Which is the above is closest to its implied volatility? What does implied volatility reflect? You are recommended to use the computer program under docsharing; do not show the computation but do show your inputs (e.g., T=?) — for this problem only.

Explanation / Answer

It is closest to 60%

Implied volatility is based on future prospective of market depends on stock price based on price changes in an option.

S0 = underlying price $30 E = strike price $27.5 = volatility (% p.a.) 0.2 ^2 = variance (% p.a.) 0.04 r = continuously compounded risk-free interest rate (% p.a.) 0.4 d = continuously compounded dividend yield (% p.a.) 0 t = time to expiration (years in %) 0.112328767 C = S × e–dt × N(d1) – E × e–Rt × N(d2) d1 = [ln(S/E) + (R – d + 2 / 2) × t] / ( × sqrt(t)) d2 = d1 – × sqrt(t) d1 = [ln($30/$27.5) + (.02 - 0 + ..04/2) × .11] / (.20 × sqrt (.11 ) 0.224871234 d2 = 0..2249 - .20 x sqrt(.11) 0.157840266 Normal Distribution N( d1) using NormDIST 0.588960276 Normal Distribution N(d2) 0.562708666 e-dt 1 e-rt 0.956062963 C = $30 x 1 x 0.5889 - $27.5 x .9561 x .5627 $2.87 S0 = underlying price $30 E = strike price $27.5 = volatility (% p.a.) 0.4 ^2 = variance (% p.a.) 0.16 r = continuously compounded risk-free interest rate (% p.a.) 0.4 d = continuously compounded dividend yield (% p.a.) 0 t = time to expiration (years in %) 0.112328767 C = S × e–dt × N(d1) – E × e–Rt × N(d2) d1 = [ln(S/E) + (R – d + 2 / 2) × t] / ( × sqrt(t)) d2 = d1 – × sqrt(t) d1 = [ln($30/$27.5) + (.04 - 0 + .16/2) × .11] / (.40 × sqrt (.11 ) 0.118082746 d2 = 0.11 - .40 x sqrt(.11) -0.01597919 Normal Distribution N( d1) using NormDIST 0.546998953 Normal Distribution N(d2) 0.493625497 e-dt 1 e-rt 0.956062963 C = $3.43 S0 = underlying price $30 E = strike price $27.5 = volatility (% p.a.) 0.6 ^2 = variance (% p.a.) 0.36 r = continuously compounded risk-free interest rate (% p.a.) 0.4 d = continuously compounded dividend yield (% p.a.) 0 t = time to expiration (years in %) 0.112328767 C = S × e–dt × N(d1) – E × e–Rt × N(d2) d1 = [ln(S/E) + (R – d + 2 / 2) × t] / ( × sqrt(t)) d2 = d1 – × sqrt(t) d1 = [ln($30/$27.5) + (.06 - 0 + ..036/2) × .11] / (.60 × sqrt (.11 ) 0.084996419 d2 = 0..2249 - .60 x sqrt(.11) -0.116096485 Normal Distribution N( d1) using NormDIST 0.533867881 Normal Distribution N(d2) 0.453788037 e-dt 1 e-rt 0.956062963 c= $4.09

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.