1 Option as Object

class Option:
  def __init__(self, position = 'long', action = 'call', strike = 0, premium = 0):
    self.position = position
    self.action = action
    self.strike = strike
    self.premium = premium
  
  def intrinsic(self, price):
    if self.position == 'long' and self.action == 'call':
      return price - self.strike
    if self.position == 'short' and self.action == 'put':
      return price - self.strike
    return self.strike - price
  
  def payoff(self, price):
    if self.position == 'long':
      return max(self.intrinsic(price), 0)
    return min(self.intrinsic(price), 0)
  
  def profit(self, price):
    if self.position == 'long':
      return self.payoff(price) - self.premium
    return self.payoff(price) + self.premium
  
  def pp_diagram(self):
    prices = list(range(0, self.strike * 2, 1))
    payoffs = [self.payoff(x) for x in prices]
    profits = [self.profit(x) for x in prices]
    fig, ax = plt.subplots()
    ax.plot(prices, payoffs, 'b')
    ax.plot(prices, profits, 'g--')
    plt.grid(color = 'silver', linestyle = '--', linewidth = 1,
             axis = 'y', alpha = 0.7)
    plt.xlabel('Price')
    plt.legend(['Payoff', 'Profit'])
    plt.show()

2 Slide 14

Let the current stock price be $35 and the European put option is in-the-money by $3.5. Find the corresponding strike price.

Solution. \(3.5=I_P(t)=K-S_t=K-35\Rightarrow K=38.5.\)

3 Slide 16

Consider a long call option with strike price K = $100. The current stock price is \(S_t\) = $105 and the call premium is $10.

1. What is the intrinsic value of the call option at time t?
2. Find the payoff and profit if the spot price at the option expiration date T is \(S_T\) = $120.
3. Draw the payoff and profit diagrams.

o1 = Option(strike = 100, premium = 10)
o1.intrinsic(105)

## 5

o1.payoff(120)

## 20

o1.profit(120)

## 10

o1.pp_diagram()

4 Slide 18

Consider a long put option with strike price K = $100. The current stock price is \(S_t\) = $80 and the put premium is $5.

1. What is the intrinsic value of the put option at time t?
2. Find the payoff and profit if the spot price at the option expiration date T is \(S_T\) = $75.
3. Draw the payoff and profit diagrams.

o2 = Option(action = 'put', strike = 100, premium = 5)
o2.intrinsic(80)

## 20

o2.payoff(75)

## 25

o2.profit(75)

## 20

o2.pp_diagram()

5 Slide 20 - P1

Consider a short position in a call option (a short call option) with strike price K = $100. The current stock price is \(S_t\) = $105 and the call premium is $10.

1. What is the intrinsic value of the short call option at time t?
2. Find the formula of the payoff and profit of the option at expiry. Compute the payoff and profit if the spot price at the option expiration date T is \(S_T\) = $120.
3. Draw the payoff and profit diagrams.

o1.position = 'short'
o1.intrinsic(105)

## -5

o1.payoff(120)

## -20

o1.profit(120)

## -10

o1.pp_diagram()

6 Slide 20 - P2

Consider a short put option with strike price K = $100. The current stock price is \(S_t\) = $80 and the call premium is $5.

1. What is the intrinsic value of the short put option at time t?
2. Find the formula of the payoff and profit of the option at expiry. Compute the payoff and profit if the spot price at the option expiration date T is \(S_T\) = $75.
3. Draw the payoff and profit diagrams.

o2.position = 'short'
o2.intrinsic(80)

## -20

o2.payoff(75)

## -25

o2.profit(75)

## -20

o2.pp_diagram()