Premier League Week Two: What Have We Learned?

Premier League Week Two: What Have We Learned?

1. Man U have bought the horses and if they can consistently run for Jose as they have for his other Year 2 teams, then they will be in the race if not in the lead. This writer along what many were shocked that Man U pipped City to get Lukaku. And Matic? What was Chelsea thinking? He has the ability to play the role that Kante played at Leicester. And certainly Chelsea recognized that? Maybe not.
2. Man City has the talent and if they get Alexis Sanchez, as predicted prior to the season they will win. I do have to say that the title chase may be an intra-Manchester contest. More clarity as these teams play better opponents.
3. Ahhh Sanchez and Arsenal. OY! Note to Arsene, take the £ and run. But do use them for other over-priced players.
And Arsenal? Perhaps this old Aerosmith ditty summarizes it:
Fate comes a-knockin’
Doors start lockin’
Your old time connection
Change your direction
You ain’t gonna change it
Can’t rearrange it
Can’t stand the pain
When it’s all the same to you, my friend

It’s the same old story
Same old song and dance, my friend
It’s the same old story
Same old story
Same old song and dance
My 5th place prediction? Certainly 3 (poor/incorrect/unfair maybe) decisions went against them, but with +77% of possession, a goal or two or three might be in order.
4. Tottenham may indeed continue to suffer the curse of Wembley. While they will not lose every game home there; they did win all their home games last year. But they looked good and are good with young – underpaid – talent. They made a good move signing defender Sanchez. Paying a fee that no doubt gave their Chairman distress, but they acted (Arsene). But that is the Market today for English Teams: Read and repeat please. Will he be enough?
5. Chelsea showed they have spirit and team continuity. But do they have the talent to run with Cavalos de Jose and Los caballos de Pep?
If not, Проща.
6. And finally a note about transfer fees, salaries, players and their teams.
Quite obviously, players have the power. Look at the shambolic situation three top teams now face with Costa, Coutinho and Sanchez. If a player does not want to play for you and as in the case of the first two, has handed in a transfer request, it is not to be anymore. Generally there is a lead up when it becomes apparent.
Is it fair when a teammate who has been shown such love by their fellows, fans, owners, community et. al. because they have played so well decides another opportunity at a club like Barcelona, or Man City, perhaps a once-in-a-lifetime one raises its head? Outside of football, we just resign with or without a contract. But our lives are not those of footballers. In both cases, however, when humans make a decision, we’ve made a decision.
Players have that power and will act. So, Jürgen and Arsene, they want to go and at least for Liverpool, he will leave the PL. One would want Sanchez
outside England, but no serious offers seemed to have been received. I have concluded that Wenger believed that with him, they could win the PL and therefore convince him to sign a new contract. Not. So, take the £ now. Arsenal will not win the PL and Sanchez will be lost. He’s a 10-month option expiring in June at the rate of the square root of time.

(https://en.wikipedia.org/wiki/Black–Scholes_model)

The Black Scholes formula is used for obtaining the price of European put and call options. It is obtained by solving the Black–Scholes PDE – see derivation below.

Using this formula, the value of a call option in terms of the Black–Scholes parameters is:

C(S,t) = SN(d_1) – Ke^{-r(T – t)}N(d_2) \,
d_1 = \frac{\ln(\frac{S}{K}) + (r + \frac{\sigma^2}{2})(T – t)}{\sigma\sqrt{T – t}}
d_2 = d_1 – \sigma\sqrt{T – t}.
The price of a put option is:

P(S,t) = Ke^{-r(T-t)} – S + (SN(d_1) – Ke^{-r(T – t)}N(d_2)) = Ke^{-r(T-t)} – S + C(S,t). \
For both, as above:

N(•) is the cumulative distribution function of the standard normal distribution
T – t is the time to maturity
S is the spot price of the underlying asset
K is the strike price
r is the risk free rate (annual rate, expressed in terms of continuous compounding)
σ is the volatility in the log-returns of the underlying