Graphs of the Black and Scholes Model:
This following graphs show the relationship between a call's premium and the underlying stock's price.
The first graph identifies the Intrinsic Value, Speculative Value, Maximum Value, and the Actual premium for a call.
![[Graph]](images/bsg1.gif)
The following 5 graphs show the impact of deminishing time remaining on a call with:
S = $48
E = $50
r = 6%
sigma = 40%
Graph # 1, t = 3 months
Graph # 2, t = 2 months
Graph # 3, t = 1 month
Graph # 4, t = .5 months
Graph # 5, t = .25 months
Graph #1
![[Graph]](images/bsgt3.gif)
Graph #2
![[Graph]](images/bsgt2.gif)
Graph #3
![[Graph]](images/bsgt1.gif)
Graph #4
![[Graph]](images/bsgt_5.gif)
Graph #5
![[Graph]](images/bsgt_25.gif)
Graphs # 6 - 9, show the effects of a changing Sigma on the relationship between Call premium and Security Price
S = $48
E = $50
r = 6%
sigma = 40%
Graph # 6, sigma = 80%
Graph # 7, sigma = 40%
Graph # 8, sigma = 20%
Graph # 9, sigma = 10%
Graph #6
![[Graph]](images/bsgs80.gif)
Graph #7
![[Graph]](images/bsgs40.gif)
Graph #8
![[Graph]](images/bsgs20.gif)
Graph #9
![[Graph]](images/bsgs10.gif)