# Bear Spread with Put Options

The **Bear Spread with Put Options** involved writing a low underlying strike price K_{1} put option and buy-in a higher underlying strike price K_{2} put option. The assumed current underlying asset price is higher than K_{2}.

## Bear Spread with Put Options

Bear Spread with Put Options with Higher Underlying Asset Price

(compute based on: put option volatility 54%, risk free rate on options 10%, K $60, K_{1} $50, K_{2} $55, period 6 months, present value of initial cashflow neglected, equity)

Profit from Bear Spread with Put Options K >> K_{2} >> K_{1}

The purpose is to profit as long as stock price is below K_{2} after compensating for initial cash outlay represented by cost of long put option and income generated by writing put option.

Given that time to expiry is the same for both options, the higher strike price put option will be price higher than the lower strike price put option.

Let us assume P_{1} be the write price of put option with underlying strike price K_{1} and P_{2} be the buy-in price put options with underlying strike price K_{2}.

### Bear Spread with Put Options

Profit Table

Initial Cash Outlay = P1 – P2 (P1 << P2)

Underlying Price Range | Payoff from Long Put Option at K_{2} strike |
Payoff from short Put Option at K_{1} strike |
Total Payoffs |

S_{T} ≤ K_{1} |
K_{2} – S_{T} |
-(K_{1 }– S_{T}) |
K_{2}– K_{1} + P_{1} – P_{2} |

K_{1} < S_{T} < k_{2} |
K_{2} – S_{T} |
0 | K_{2} – S_{T} + P_{1} – P_{2} |

S_{T} ≥ K_{2} |
0 | 0 | P_{1} – P_{2} |

In the model of Bear Spread with Put Options, there will be a loss resulting from initial cash outlay if underlying asset prices rises above K_{2} after expiry of options. There will be profit if price of underlying ends below K_{1}. This profit comes entirely from cash inflow from writing put option after deducting cost of buying put options.

### Three types of Bear Spread with Put Options can be distinguished

- Both puts are initially out of the money
- One put is initially in the money; the other call (put) is initially out of money
- Both puts are initially in the money

The highest risk and reward Bear Spread with Put Options comes from type 1. They cost very little to set up because they are out of the money but have small probability of giving high payoffs K_{2} – K_{1 }+ P_{1 }– P_{2 }(where P_{1} << P_{2} and P_{1}😛_{2} => 0)

Bear Spread with Put Options with Lower Underlying Asset Price

(compute based on: put option volatility 54%, risk free rate on options 10%, K $45, K_{1} $50, K_{2} $55, period 6 months, present value of initial cashflow neglected, equity)

Profit from Bear Spread With Put Options K << K_{1} << K_{2}

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