SPS HOLDINGS 2006 Opt’95 1 Basics of Capital Markets AXA Belgium 2006 Options Presentation

SPS HOLDINGS 2006 Opt’95 2 Pricing an Option Portfolio 1: C + XD = V 1 Portfolio 2: P + S = V 2 where C = Value of a Call XD = Discounted Exercise Price P = Value of a Put S = A share of the underlying S*= Spot Price at Expiry Portfolio 1 must equal Portfolio 2 V 1 = V 2

SPS HOLDINGS 2006 Opt’95 3 Arbitrage Relationship for Put-Call Parity S* X V1 = C + XD O + X (S*-X) + X V2 = P + S (X-S*) + S* O + S* V1 = X V1 = S* V2 = X V2 = S* V1 = V2 IN BOTH

SPS HOLDINGS 2006 Opt’95 4 Thus: V 1 = V 2 C+XD = P+S C-(S-XD) = P and since S-XD = FORWARD (F) C-F = P F = C-P - F = P-C

SPS HOLDINGS 2006 Opt’95 5 Long a Call Long a F orward Short a Put F = C - P 45o S $

SPS HOLDINGS 2006 Opt’95 6 Creating the Forward Long a Call Long a F orward Short a Put F = C - P 45o S $

SPS HOLDINGS 2006 Opt’95 7 Short a Forward Short a Call Long a Put S $ -F = P-C

SPS HOLDINGS 2006 Opt’95 8 Creating the Forward Short a Forward Short a Call Long a Put S $ -F = P-C

SPS HOLDINGS 2006 Opt’95 9 Valuing the Option Today - Using Intuition Day 0 Day % Share Price At Expiry Value of Call At Expiry $ 105 $ 5 $ 95 $ 0

SPS HOLDINGS 2006 Opt’95 10 CREATE AN ARBITRAGE PORTFOLIO S C 2C S-2C So no matter what happens - S = 105 or S = 95  S - 2C = 95

SPS HOLDINGS 2006 Opt’95 11 On Day 1 S-2C = 95But What About Day 0? S - 2C If ( C) day 0 > (95) day 1 Then ( C) day 0 = (95) day r 2C = (95) 1 + r if r = 7.5% C = $2.51

SPS HOLDINGS 2006 Opt’95 12 Through the Arbitrage Portfolio it is clear that as the Interest Rate Rises (r ) the Value of a Call Rises ( C ).

SPS HOLDINGS 2006 Opt’95 13 Alternatively, one can see graphically As XD < X and C = S* - XD (intrinsic value) Then the greater r XD smaller C = S* - XD is larger XD X $ S

SPS HOLDINGS 2006 Opt’95 14 From this diagram, intuitively As T = Time 0 the XD X therefore C if XD C the greater T where T = time to expiry

SPS HOLDINGS 2006 Opt’95 15 C = $ S XD

SPS HOLDINGS 2006 Opt’95 16 Finding the Value given the Volatility C = $ S XD

SPS HOLDINGS 2006 Opt’95 17 If XD, S, T are held constant, then as the C?

SPS HOLDINGS 2006 Opt’95 18 Volatility is Why Options Exist! Without it We could give them Away!!! Can you think of examples Where someone would be so stupid???

SPS HOLDINGS 2006 Opt’95 19 Finally: OR

SPS HOLDINGS 2006 Opt’

SPS HOLDINGS 2006 Opt’95 21 From Put/Call Parity P = C - S + XD C( S, X, T, r, σ ) d (XD) = d ( r, T ), - P = P (S, X, T, r, σ ) - + ? ? + But Note then