aggregate multipliers
description
prototypes
example 1:
share = 10
aggregate call = 20
-> 10x = 20
-> x = 2
aggregate put = 5
-> 10x = 5
-> x = 1/2
therefore by reciprocity:
put multiplier 0.5 == call multiplier 2.0 -> True
put call
1/2 <-> 2/1
example 2:
share price = 10
calls
|
strike ask open | bet confidence commitment
10 4 1 | 14 4 64
15 2 1 | 17 2 34
20 1 1 | 21 1 21
call bet = strike + ask
confidence = ask
commitment = bet * confidence
commitment sum = 64 + 34 + 21 = 119
confidence sum = 4 + 2 + 1 = 7
union = confidence sum / commitment sum = 119 / 7 = (>=) 17
(aggregate break even)
union multiplier
= union / share price
= 17 / 10 = 1.7x
puts
|
strike ask open | bet confidence commitment
5 2 1 | 3 2 6
10 4 1 | 6 4 24
put bet = strike - ask
confidence = ask
commitment = bet * confidence
commitment sum = 6 + 24 = 30
confidence sum = 2 + 4 = 6
union = confidence sum / commitment sum
= 30 / 6
= 5
put union multiplier
= union / share price
= 5 / 10
= 1/2
therefore:
before reciprocity:
calls = 1.7x
puts = 0.5x
after reciprocity:
calls = 1.7x
puts = 2.0x
Therefore the puts are more expensive than the calls
and thus are perhaps favored.