# Bull Spread with Call Options

The **Bull Spread with Call Options** involved selling a call option at strike price K_{2} and buy in a call option at lower strike price K_{1}. The assumed current underlying asset price, K, is higher than K_{2}.

## Bull Spread with Call Options

(compute based on: call 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)

Bull Spread with Call Options K >> K_{2} >> K_{1}

The purpose is to profit as long as stock price moves above K_{1} after compensating for initial cash outlay represented by cost of long call option and income generated by writing call option.

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

Let us assume P_{1} be buy-in price of call option with underlying strike price K_{1} and P_{2} writing price of call option with underlying strike price K_{2}.

### Bull Spread with Call Options

Profit Table

Initial Cash Outlay = -P1+P2 (P1>>P2)

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

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

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

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

In the model of Bull spread using call options, there will be a loss resulting from initial cash outlay if underlying asset prices comes in below K_{1} after expiry of options. There will be profit if price of underlying ends above K_{2}.

### Three types of Bull Spreads with call options can be distinguished

- Both calls are initially out of the money
- One call is initially in the money; the other call is initially out of money
- Both calls are initially in the money

The highest risk and reward Bull Spread 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)

Bull Spread with Call Options with Lower Underlying Asset Price

(compute based on: call 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 Bull Spread With Call Options K << K_{1} << K_{2}

Best Options Trading for Dummies profits on Bull Spread with Call Options using Options Trading 101.