Put Warrant Pricing

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Overview

Put Warrant pricing follows similar principles to Call Warrants but with inverse directional characteristics. The price reflects the market’s expectation of downside risk.

Price Interpretation

What Does the Price Mean?

A Put Warrant price of $0.25 can be interpreted as:

Interpretation	Explanation
Implied Probability	~25% chance underlying falls below strike
Hedge Cost	Pay $0.25 to protect $1.00 of downside
Premium Yield	Writers earn 25% premium for taking downside risk

Pricing Factors

1. Intrinsic Value

Intrinsic Value = max(0, (Strike - Current Valuation) / Strike)

Example:
Current Valuation: $150B (Oracle)
Strike: $180B
Intrinsic Value = ($180B - $150B) / $180B = 16.7%

Minimum warrant price ≈ $0.167 (plus any time value)

2. Time Value

For puts, time value reflects probability of favorable (downward) movement:

Put Time Value Factors:
├── More time → Higher time value (more chance to decline)
├── Higher volatility → Higher time value
├── Higher interest rates → Slightly lower put value
└── Distance from strike → Non-linear impact

3. Volatility Premium

Put writers demand higher premiums for volatile underlyings:

Volatility Level	Premium Multiplier
Low (< 30%)	1.0x
Medium (30-50%)	1.2x
High (50-70%)	1.5x
Very High (> 70%)	2.0x

Put Premium Pricing

Writer’s Perspective

Put writers (platform pool + KYB writers) price puts based on:

Put Premium = Base Rate + Risk Premium + Time Premium + Liquidity Premium

Where:
Base Rate = Risk-free rate × Time (5% annualized)
Risk Premium = f(Volatility, Strike Distance, Underlying Quality)
Time Premium = f(Days to Expiry)
Liquidity Premium = f(Pool Depth, Demand)

Expected Yield Matrix

Strike Distance	3 Month	6 Month	12 Month
ATM (0%)	8-12%	15-20%	25-35%
OTM-10%	5-8%	10-15%	18-25%
OTM-20%	3-5%	6-10%	12-18%

Yields are annualized. Actual returns depend on outcome.

Premium Calculation Example

Scenario: SpaceX Put at $150B Strike

Inputs:
├── Current Valuation: $180B
├── Strike: $150B (17% OTM)
├── Time to Expiry: 6 months
├── Implied Volatility: 50%
└── Risk-free Rate: 5%

Premium Calculation:
├── Base Rate: 5% × 0.5 = 2.5%
├── Volatility Premium: 50% × 0.3 = 15%
├── Strike Distance Discount: -17% × 0.5 = -8.5%
├── Liquidity Premium: +2%
└── Total Premium: ~11%

Put Warrant Price: ~$0.11 per token

Yield for Writer

If writer sells $100K notional of puts:
├── Collateral required: $100K USDC
├── Premium received: $11K (11%)
├── Time period: 6 months
└── Annualized yield: 22%

Outcome A (OTM - SpaceX stays above $150B):
├── Writer keeps premium: +$11K
├── Collateral returned: $100K
└── Total return: +11% (22% annualized)

Outcome B (ITM - SpaceX at $120B):
├── Premium received: +$11K
├── Payout to buyers: -$20K [($150B-$120B)/$150B × $100K]
├── Net P&L: -$9K
└── Total return: -9%

AMM Price Discovery

Pool Mechanics

Put warrant pools use the same CPMM as calls:

x × y = k

Where:
x = Put warrant token reserve
y = USDC reserve

Price Dynamics

Put Price Increases When:
├── More buyers (demand for protection)
├── Bad news about underlying
├── Market-wide risk-off sentiment
├── Approaching exercise window
└── Writers withdraw liquidity

Put Price Decreases When:
├── More sellers (holders taking profits)
├── Good news about underlying
├── Market-wide risk-on sentiment
├── Long time to expiry
└── Writers add liquidity

Put-Call Relationship

Theoretical Parity

In efficient markets, put and call prices are related:

C + PV(K) = P + S

Rearranged for Put:
P = C + PV(K) - S

For PIPO (simplified):
Put Price ≈ Call Price + Strike Discount - Valuation Premium

Practical Implications

Market Condition	Put vs Call
Bullish consensus	Calls expensive, puts cheap
Bearish consensus	Puts expensive, calls cheap
Neutral/uncertain	Similar pricing
High volatility	Both expensive

Pricing Examples

Example 1: ATM Put

Underlying: SpaceX
Oracle Valuation: $180B
Strike: $180B (ATM)
Time to Expiry: 6 months

Components:
├── Intrinsic Value: $0.00
├── Time Value: ~$0.28
├── Volatility Premium: ~$0.07
└── Total Price: ~$0.35

Interpretation:
- 35% probability SpaceX drops below $180B
- Hedgers pay 35% to protect against decline

Example 2: OTM Put (Cheap Hedge)

Underlying: SpaceX
Oracle Valuation: $180B
Strike: $150B (17% OTM)
Time to Expiry: 6 months

Components:
├── Intrinsic Value: $0.00
├── Time Value: ~$0.08
├── Volatility Premium: ~$0.03
└── Total Price: ~$0.11

Interpretation:
- 11% probability SpaceX drops below $150B
- Cheap tail-risk protection
- High leverage if disaster occurs

Example 3: ITM Put (After Down-Round)

Underlying: SpaceX
Oracle Valuation: $150B (down from $180B)
Strike: $180B
Time to Expiry: 3 months

Components:
├── Intrinsic Value: ~$0.17 [($180B-$150B)/$180B]
├── Time Value: ~$0.08
└── Total Price: ~$0.25

Interpretation:
- Already profitable, can exercise in next window
- Time value reflects chance of further decline

Writer Dashboard Pricing

Premium Opportunities

┌─────────────────────────────────────────────────────────────────┐
│              PUT WRITING OPPORTUNITIES                          │
├─────────────────────────────────────────────────────────────────┤
│                                                                 │
│  Underlying      Strike    Expiry    Premium   Ann. Yield       │
│  ───────────────────────────────────────────────────────────   │
│  SpaceX          $150B     Q42025    11.2%     22.4%           │
│  SpaceX          $160B     Q42025    14.5%     29.0%           │
│  OpenAI          $60B      Q22026    18.3%     18.3%           │
│  Stripe          $50B      Q32025    9.8%      39.2%           │
│                                                                 │
│  Sorted by: [Yield ▼] [Risk] [Expiry] [Underlying]             │
│                                                                 │
│  [View Details] [Write Put]                                     │
│                                                                 │
└─────────────────────────────────────────────────────────────────┘

Dynamic Premium Adjustment

Event-Driven Pricing

Event	Premium Impact
Funding round announced	-20% (bullish signal)
IPO filing	-30% (liquidity coming)
Key executive departure	+50% (uncertainty)
Lawsuit/regulatory action	+100% (risk spike)
Down-round rumor	+75% (validation of bears)

Automated Adjustment

Premium Adjustment Algorithm:
├── Monitor news feeds (RSS, Twitter, Bloomberg)
├── Sentiment analysis scoring
├── If significant event detected:
│   ├── Calculate sentiment impact
│   ├── Adjust pool parameters
│   └── New premium = Base × (1 + Impact Score)
└── Manual override by Oracle Committee if needed

Risk Metrics for Writers

Greeks (Simplified)

Greek	Put Impact	Interpretation
Delta	-0.3 to -0.7	Sensitivity to underlying
Theta	Positive	Time decay benefits writer
Vega	Negative	Volatility spike hurts writer
Gamma	Context-dependent	Acceleration of delta

Risk Dashboard

┌─────────────────────────────────────────────────────────────────┐
│              WRITER RISK METRICS                                │
├─────────────────────────────────────────────────────────────────┤
│                                                                 │
│  Position: SPACEX-PUT-150B-Q42025 ($100K written)              │
│                                                                 │
│  Greeks:                                                        │
│  ├── Delta: -0.35 (lose $35K per 10% drop)                     │
│  ├── Theta: +$150/day (earn from time decay)                   │
│  ├── Vega: -$800 per 1% vol increase                           │
│  └── Gamma: -0.02                                               │
│                                                                 │
│  Scenarios:                                                     │
│  ├── SpaceX +10%: +$11K (keep premium)                         │
│  ├── SpaceX flat: +$11K (keep premium)                         │
│  ├── SpaceX -10%: +$8K (partial premium)                       │
│  ├── SpaceX -20%: -$2K (small loss)                            │
│  └── SpaceX -30%: -$12K (significant loss)                     │
│                                                                 │
│  Breakeven: $139B valuation (-22.8% from current)              │
│                                                                 │
└─────────────────────────────────────────────────────────────────┘

API Reference

Get Put Quote (Buyer)

const quote = await pipo.getQuote({
  warrant: 'SPACEX-PUT-150B-Q42025',
  side: 'BUY',
  amount: 1000
});

// Response
{
  premium: 110.50, // USDC total
  pricePerToken: 0.1105,
  impliedYield: 22.1, // % annualized (for writer)
  breakeven: 139000000000, // $139B
  maxPayout: 1000, // USDC if valuation goes to $0
  fee: 0.33 // USDC (0.3%)
}

Submit Put Write (Writer)

const tx = await pipo.writePut({
  underlying: 'SPACEX',
  strike: 150000000000, // $150B
  expiry: 'Q42025',
  notional: 100000, // $100K
  minPremium: 10000 // Accept at least $10K premium
});

// Response
{
  txHash: '0x...',
  collateralLocked: 100000,
  premiumReceived: 11200,
  annualizedYield: 22.4,
  tokensIssued: 100000,
  expiryDate: '2025-12-31'
}