文档介绍：
European Options on Stocks Paying
Continuous Dividends
• The following two cases lead to identical stock
Topic 11 price distribution at time T
– The stock starts at price S and pays a continuous
Options on Stock Indices, Currencies dividend yield at rate q
– The stock starts at price Se–q T and pays a continuous
dividend yield at rate q
Chapter 12
• A Simple Rule
We can value European options by reducing the
stock price to Se–q T and then treat it as though
there is no dividend
Financial Engineering, Lingnan College, 1999 Undergraduate Class, Spring 2002, by Prof. NIU Hong Financial Engineering, Lingnan College, 1999 Undergraduate Class, Spring 2002, by Prof. NIU Hong
European Options on Stocks Paying Extension of Bounds and Call-Put Parity
Continuous Dividends,cont’d in Chapter 8
­rT
Lower Bound for calls: c ³ S ­ PV (D) ­ Xe
c = Se­qT N(d ) ­ Xe­rT N (d )
1 2 c ³ Se­qT ­ Xe­rT
­qT ­rT
ln(Se / Xe ) 1 2
where d1 = + σ T ­rT ­qT
σ T 2 Lower Bound for puts p ³ Xe ­ Se
­rT
d2 = d1 ­σ T p ³ Xe ­ (S ­ PV (D))
­ rT
Put-Call Parity c+ Xe = p+ S ­ PV(D)
p = Xe­rT N(­d ) ­ Se­qT N(­d )
2 1 c+ Xe­ rT = p + Se­qT
Financial Engineering, Lingnan College, 1999 Undergraduate Class, Spring 2002, by Prof. NIU Hong Financial Engineering, Lingnan College, 1999 Undergraduate Class, Spring 2002, by Prof. NIU