MFE Lesson 11 slides

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

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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...
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