04 v call price at time to expiry t is ct calculate

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: unded risk-free rate is 0.04 (v) Call price at time to expiry t is Ct Calculate the implied volatility of such options using the BS model. 23 / 25 Example 11.4. Solution. 50 50e 0.04t + (0.04 + 0.5 2 )t p = t p 0.04t + 0.04t + 0.5 2 t p = = 0.5 t t p p p d2 = 0.5 t t = 0.5 t = d1 d1 = ln Ct = 50N (d1 ) 50e 0.04t · e = 50N (d1 ) 50 (1 Ct + 50 N ( d1 ) = 100 0.04t N ( d1 ) = N (d1 )) = 100N (d1 ) 50 24 / 25 Example 11.4. Solution (cont.) For example, if Ct = 3.98 as time to expiry t = 0.25, then 3.98 + 50 N (d1 ) = = .5398 ) d1 = 0.1 , 100 p 0.5 0.25 = 0.1 , = 0.4 If Ct = 5.96 as time to expiry t = 1, then 5.96 + 50 = .5596 ) d1 = 0.15 , 100 0.5 = 0.15 , = 0.3 N ( d1 ) = If Ct = 7.14 as time to expiry t = 2, then 7.14 + 50 N ( d1 ) = = .5714 ) d1 = 0.18 , 100 p 0.5 2 = 0.18 , = 0.255 25 / 25 Example 11.4. Conclusion. Note that in this example the implied volatility declined as the time to expiry increased. This is a typical pattern. In addition, the implied volatility tends to decrease as the strike price increases. 26 / 25...
View Full Document

Ask a homework question - tutors are online